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CARNEGIE  INSTITUTION  OF  WASHINGTON 

Publication  No.  383 


UNivmsiiy  of  Illinois 


1927 


J.  B.  LIPPINCOTT  COMPANY 
EAST  WASHINGTON  SQUARE 
PHILADELPHIA,  PENNA. 


ACOUSTIC  EXPERIMENTS  WITH  THE  PIN-HOLE 
PROBE  AND  THE  INTERFEROMETER 

U-GAGE 


BY 

CARL  BARUS 

Professor  of  Physics,  Emeritus ,  in  Brown  University 


Published  by  the  Carnegie  Institution  of  Washington 

Washington,  1927 


. 

PREFACE 


The  pin-hole  probe  (a  finely  perforated  plate  or  cone  mounted  on  a  quill- 
tube  as  described  in  the  preceding  Reports*)  measures  the  residual  nodal 
intensity  or  potential  energy  per  cubic  centimeter,  at  any  point  along  the  axis 
of  a  stationary  soundwave,  by  the  aid  of  an  interferometer  U-gage  of  mercury. 
The  pressure  indicated  by  the  displacement  (s)  of  white-light  fringes  is  therefore 
a  maximum  at  any  node  and  falls  off  harmonically  to  zero  at  the  succeeding 
antinodes.  Progressive  waves  are  without  effect  on  the  probe.  It  is  advisable 
to  use  small  fringes  (o.oi  cm.  in  the  ocular  of  the  telescope),  so  that  one  scale- 
part  may  be  roughly  io-6  atm.,  or  5  nearly  standardized  in  dynes/cm2. 

In  view  of  the  large  number  of  tests  made  in  the  lapse  of  the  present 
experimental  investigation,  the  only  practical  method  of  communicating  the 
results  is  by  the  way  of  graphs.  To  facilitate  the  reading  of  these,  inserts 
showing  the  character  of  the  apparatus  or  the  method  employed  accompany 
the  graphs  in  all  essential  cases,  in  order  that  anyone  interested  may  get 
much  of  the  information  under  consideration  from  this  inspection.  To  sum¬ 
marize  the  contents  of  the  present  experimental  report  otherwise  seems 
hardly  feasible. 

It  is  to  be  understood  that  the  purpose  of  the  experiments  is  an  orientation 
of  the  acoustic  phenomena,  the  tryout  of  a  method  under  conditions  as  varied 
as  possible.  The  excitation  of  organ-pipes  by  telephone  is  an  efficient  and 
sometimes  the  only  method  available  in  the  furtherance  of  this  aim,  as 
anything  of  the  nature  of  air-currents  would  be  fatal.  Large  inductances 
were  therefore  needed,  and  I  used  iron-cored  coils  because  of  their  con¬ 
venience  and  as  presumably  adequate  for  the  purposes  specified.  Though 
certain  inductance  measurements  are  attempted  acoustically,  these  are  used 
as  illustrations  only;  for,  ultimately,  the  pin-hole  probe  can  not  of  course 
compete  with  the  galvanometer  or  the  ear.  Later,  I  had  frequent  occasion 
to  regret  the  use  of  iron-cored  coils,  for  the  pin-hole  probe  work  came  out 
better  than  I  had  anticipated  and  would  have  sufficed  for  more  satisfactory 
electric  work  than  the  coils  permitted. 

Inductions  treated  acoustically  by  differential  telephones  in  Chapter  I, 
therefore,  gave  crude  results  only.  On  the  other  hand,  the  experiments 
showing  continuous  change  of  reflection  without,  into  reflection  with  change 
of  phase,  of  the  continuous  change  of  the  phase  relations  of  the  two  cooperat¬ 
ing  telephone-plates  (Para,  n,  et  seq.)  make  an  interesting  exhibit,  I  think. 
In  the  final  sections  of  the  chapter  much  work  was  done  with  the  object  of 
specifying  the  induction  phenomena  from  the  location  of  crests  and  troughs  of 
the  acoustic  graphs,  from  their  intersections,  from  zero  and  exchange  devices, 
etc.  I  did  not,  however,  in  spite  of  the  sharply  delineated  graphs,  reach  sat¬ 
isfactory  solutions  for  the  problems  involved. 

*  Carnegie  Inst.  Wash.  Pub.  No.  310,  Washington,  D.  C.;  Part  I,  1921;  Part  II,  1923; 
Part  III,  1924 


VI 


PREFACE 


The  preceding  experiments  had  already  indicated  the  incidental  occur¬ 
rence  of  electric  oscillation.  Direct  telephonic  coupling  of  acoustic  and 
electric  oscillations  were  thus  suggested.  In  Chapter  II  a  condenser  is 
inserted  into  the  circuit  which  energizes  the  telephones,  to  facilitate  the  inter¬ 
pretation  of  results.  The  graphs,  in  fact,  become  more  precise  and  are  more 
satisfactorily  construed.  At  first  a  motor-break  was  used  as  an  interrupter 
in  the  primary.  Later  an  ordinary  platinum-spring  break  released  the  vibra¬ 
tions  and  gave  surprisingly  steady  service.  The  purpose  of  using  electric 
oscillations  to  interpret  the  anomalous  presence  of  apparently  low  notes  in 
short  and  slender  pipes  has  in  a  measure  succeeded. 

Pin-hole  probes  may  be  used  singly,  if  they  open  out  from  a  closed  air 
region  vibrating  acoustically.  As  a  rule,  it  is  advantageous  to  use  them  in 
pairs,  in  which  case  they  may  be  set  either  to  cooperate  with  or  to  oppose  each 
other.  Chapter  III  gives  a  summary  of  remarkably  varied  results  obtained 
with  paired  pin-hole  probes,  and  it  was  hoped  that  these  experiments  would 
throw  definite  light  on  the  phenomena  as  a  whole.  What  they  do  exhibit  is  the 
important  function  of  the  quill-tube  prolongation  or  connection  on  either  side 
of  the  pin-hole.  So  much  is  this  the  case  that  paired  quill-tubes,  without 
pin-hole  constriction  but  of  suitable  lengths,  may  be  made  to  function,  though 
the  pressure  produced  is  relatively  feeble.  The  presence  of  a  constriction, 
however,  even  if  perfectly  cylindric  like  a  very  short  end  of  capillary  tube, 
enhances  the  result.  One  suspects  that  the  production  of  vortices  on  the 
inside  of  the  probe  at  the  shoulder  and  node  is  the  ultimate  cause  of  pin-hole 
or  constriction  phenomena.  Such  vortices  decrease  the  outflow  by  locking 
up  a  part  of  its  translatory  energy  in  eddies.  In  other  words,  the  excess  of 
the  flow  alternating  across  and  through  the  pin-hole  walls  is  into  the  region 
of  excess  vorticity.  At  the  end  of  Chapter  IV  (Para.  90,  et  seq.)  this  view  is 
in  a  measure  confirmed  by  pin-holes  pricked  in  the  thinnest  sliver  of  mica. 
Even  if  cemented  between  identical  quill-tubes,  this  ideally  thin  pin-hole 
has  exceptionally  efficient  but  opposed  properties  on  its  two  sides.  Although 
acoustic  pressure  may  be  built  up  in  a  region  of  almost  any  volume  and  in  a 
surprisingly  short  time,  provided  its  boundaries  are  closed  and  rigid,  the 
pin-hole  probe  can  not  be  used  to  produce  a  persistent  flow  of  air  into  an 
expansible  region  of  constant  pressure,  even  though  below  that  producible  by 
the  probe.  This  may  be  neatly  shown  with  regions  closed  with  liquid  films. 

The  short  and  slender  air-columns  used  in  the  above  experiments  are 
without  influence  on  the  telephone-plates  and  at  their  mercy,  as  it  were. 
The  case  of  relatively  massive  air-columns  should  be  different.  The  be¬ 
havior  of  a  closed  organ-pipe  of  variable  depth,  blown  without  the  pres¬ 
ence  of  air-currents  within,  is  first  treated,  with  the  necessary  reference  to 
the  quill-tube  connection  with  the  U-gage.  The  exploration  of  nodal  inten¬ 
sity  at  different  depths  below  the  mouth  in  case  of  horns,  cylindrical  tubes, 
follows.  These  are  blown  by  the  telephone.  Two  methods  of  varying  the 
pitch  of  the  telephone  are  contrasted:  the  motor-break  giving  the  pitch 
directly  and  the  spring-break  with  an  oscillating  circuit  giving  pitch  indirectly. 


PREFACE 


Vll 


The  results  of  the  two  procedures  differ  more  widely  than  one  would  anticipate. 
In  the  latter  case  it  is  observed  that  the  graphs  obtained  frequently  consist  of 
linear  elements,  particularly  in  the  case  where  circuits  are  rhythmically 
charged  and  discharged.  As  the  cylindrical  pipe  offers  good  opportunities 
for  the  comparison  of  salient  and  reentrant  pin-hole  probes,  both  of  the 
conical  and  plate  types,  such  tests  (as  already  instanced)  are  carried  out.  The 
use  of  mica  plates  makes  it  possible  to  increase  the  sensitivity  of  the  latter 
even  above  the  conical  type,  though  this  is  always  more  expeditious. 

In  the  last  chapter  a  number  of  incidental  investigations  are  grouped 
together.  The  first  of  these  treats  the  pressure  of  the  electric  wind  driven 
from  a  highly  charged  point  upon  an  opposed  electrode  connecting  with 
the  U-tube  interferometer.  The  results  point  out  the  efficiency  of  the  mucro- 
nate  electrode,  as  it  may  be  called,  in  which  a  sharp  point  projects  about  half 
a  millimeter  from  the  electrode.  The  axial  pressure  of  the  ionized  convection 
current,  when  checked  by  the  opposed  electrode,  may  be  increased  io  or  even 
20  times  by  this  device,  which  seems  to  dip  into  an  anode  or  cathode  mini¬ 
mum.  Pressure  ceases  instantly  on  the  occurrence  of  sparks  or  any  sputtering. 

A  tentative  method  for  the  measurement  of  the  energy  of  X-rays  was 
tried  out,  but  it  failed  because  of  contemporaneous  temperature  discrepan¬ 
cies.  Finally  a  promising  modification  of  the  U-gage  was  also  a  disappoint¬ 
ment,  because  it  could  not  be  freed  from  the  capillary  adhesion  of  parts. 


Carl  Barus. 


— 


CONTENTS 


Chapter  I — Short  and  Slender  Air-columns.  Circuits  Without  Explicit 

Capacity 

PAGE 

1.  Circuits.  Figs,  i  to  5 .  1 

2.  Table  of  inductances .  1 

3.  Survey  in  pitch.  Figs.  6  to  10 .  2 

4.  Continuous  change  of  phase  difference.  Fig.  11 .  3 

5.  Phase  difference  apparently  passing  through  zero.  Figs.  12  to  14 .  4 

6.  Phase  reversal  owing  to  inductance.  Figs.  15  to  17 .  5 

7.  Data.  Fig.  18 .  6 

8.  The  equations  completed.  Single  circuit .  8 

9.  Circuits  in  phase  and  in  sequence .  8 

10.  Improvement  of  telephones.  Figs.  19  and  20 .  9 

1 1 .  Comparison  of  primary  and  secondary.  Figs.  2 1  to  30 .  9 

12.  Layers  of  transformer  in  parallel.  Figs.  3 1  to  36 .  1 1 

13.  Single  half  layer.  Fig.  37 .  14 

14.  Incidental  origin  of  initial  phase  differences.  Figs.  38  to  41 .  14 

1 5.  Circuits  without  transformer.  Figs.  42  to  44 .  16 

16.  Telephone-plate  subject  to  an  external  magnetic  field.  Fig.  45 .  17 

1 7.  Remarks.  Figs.  46  to  48 .  17 

18.  Zero  methods.  Primary  and  secondary.  Fig.  49 . : .  18 

19.  Primaries  only.  Figs.  50  to  54 .  19 

20.  Zero  method  with  the  secondary.  Figs.  55  and  56 .  21 

2 1 .  Exchange  of  loads.  Circuits  in  parallel.  Figs.  57  to  62 .  21 

22.  Further  experiments.  Figs.  63  to  71 .  23 

23.  Summary.  Quantitative  considerations.  Fig.  72 .  26 

24.  High-resistance  telephones.  Zero  methods.  Figs.  73  to  75 .  29 

25.  The  same  with  small  inductor.  Figs.  76  to  79 .  31 

26.  Compensating  inductances.  Fig.  80 .  33 

27.  Same  without  commutator.  Figs.  81  and  82 .  34 

28.  Electrolytic  resistances.  Figs.  83  to  85 .  36 

29.  Single  circuits  isolated.  Figs.  86  and  87 .  37 

30.  Data . 39 

31 .  Troughs  of  the  paired  graphs .  40 

32 .  The  intersection  of  paired  graphs . . .  41 

33.  Parallel  circuits  actuated  by  single  inductor  open  circuits.  Figs.  88  to  95 . 43 

34.  Minima  and  intersections .  45 

35.  Resistances  in  the  air-gap  2,3.  Double  symmetrical  inductor.  Fig.  96 .  46 

Chapter  II — Short  and  Slender  Air-columns.  Circuits  with  Localized 

Capacity 

36.  Capacities  in  the  air-gap.  Figs.  97  and  98 .  47 

37.  Single  inductor,  unsymmetrical.  Figs.  99  to  101 .  49 

38.  Effect  of  the  lower  harmonics.  Figs.  102  to  105 .  51 

39.  Detailed  survey  near  the  crest.  Figs.  106  to  1 12 .  53 

40.  Non-coupled  inductances  inserted.  Reductions.  Fig.  1 13 .  55 

41.  Low-resistance  telephones.  Fig.  1 14 .  57 

42.  Spring  mercury  contact-breaker  of  inaudibly  low  pitch.  Figs.  1 1 5  and  1 16 .  59 

43.  Inductor  with  variable  core.  Figs.  1 17  to  120 .  60 

44.  Increased  currents.  Figs.  12 1  to  123 .  62 

45.  Longer  and  wider  organ-pipe.  Figs.  124  and  125 .  63 

46.  Long  thin  pipe.  Figs.  126  and  127 .  64 

47.  Short  thin  pipe.  Figs.  128  to  130 .  66 

48.  Long  and  short  pipes  compared.  Combined  primaries.  Figs.  131  and  132 .  67 

49.  Opposed  mutual  inductions  and  similar  comparisons.  Figs.  133  to  135 .  69 

50.  Primaries  in  parallel.  Fig.  136 .  71 

Chapter  III — Mutual  Relations  of  Pin-hole  Probes.  Quill-tubes 

5 1 .  Outer  pin-hole  of  the  pipe  enlarged.  Figs.  137  and  138 .  73 

52.  Reversal  of  outer  pin-hole  probe.  Figs.  139  to  142 .  74 

53.  The  same.  Cases  of  smaller  length  increments.  Figs.  143  to  153 .  76 

ix 


X 


CONTENTS 


Chapter  III — Mutual  Relations  of  Pin-hole  Probes.  Quill-tubes — Continued 

PAGE 

54.  The  same.  Summary.  Fig.  151 .  80 

55.  Pin-holes  in  series.  Change  of  length  and  electric  capacity.  Figs.  155  to  160 .  82 

56.  Effect  of  the  number  of  pin-holes.  Figs.  163  to  167 .  84 

57.  Outer  quill-tubes  of  varying  lengths,  all  open.  Figs.  1 61  and  162 .  87 

58.  Data  for  identical  reentrant  plate  pin-hole  probes  of  different  lengths.  Figs.  168 

toi7i .  88 

59.  Inner  quill  and  outer  conical  glass  pin-hole.  Fig.  172 .  92 

60.  Cooperating  quill-tubes  without  pin-holes.  Figs.  1 73  to  1 78 .  93 

61.  Reversal  of  the  preceding  adjustment.  Figs.  179  to  1 81 .  95 

62.  Quill -tubes  of  constant  external  diameter,  reduced  in  length  and  bore  conjointly. 

Figs.  182  to  185 .  97 

63.  Acoustic  pressures  in  case  of  a  soap-bubble.  Figs.  186  and  187 .  100 

Chapter  IV — Pipes  with  Relatively  Massive  Air-columns.  Organ-pipes.  Horns 

64.  Pin-hole  record  for  variable  organ-pipe.  Apparatus.  Fig.  188 .  102 

65.  Results.  Fig.  189 .  102 

66.  Further  experiments.  Figs.  190  and  19 1 .  103 

67.  Reduced  diameter  of  pin-hole  probe  connector.  Fig.  192 .  105 

68.  Steady  blast.  Figs.  193  and  194 .  107 

69.  Miscellaneous  tests .  109 

70.  Mean  total  pressure  in  organ-pipe.  Soap-film.  Fig.  195 .  no 

71.  Same.  Direct  U -gage  measurement.  Fig.  196 .  in 

72.  Acoustics  of  the  conical  horn.  Apparatus.  Broad  horn.  Figs.  197  and  198 .  in 

73.  Results  for  horn.  Figs.  199  to  204 .  113 

74.  Slender  horn  (70) .  Figs.  205  to  2 1  o .  115 

75.  Cylindrical  pipe.  Figs.  211  to  218 . 117 

76.  Extensible  pipe.  Figs.  219  to  223 .  119 

77.  Closed  organ-pipe.  Figs.  224  and  225 .  12 1 

78.  Alternating  current.  Figs.  226  and  227 . 122 

79.  Remarks .  124 

80.  Charging  circuit.  Figs.  228  to  230.  . .  125 

81.  Reentrant  pin-hole  probe.  Figs.  231  to  236 .  127 

82.  The  same;  s  and  x  graphs.  Figs.  237  to  239 . 129 

83.  The  same;  direct  tests.  Figs.  241  to  243 .  130 

84.  Plate  pin-hole  with  anterior  and  posterior  quill-tubes.  Fig.  240 .  13 1 

85.  The  same;  plate  pin-hole  reversed.  Figs.  244  and  245 .  133 

86.  The  same;  further  experiments.  Figs.  246  to  250 .  133 

87.  Salient  glass  pin-hole  with  anterior  quills.  Figs.  251  to  256 .  135 

88.  Rear  quill-tubes  variable.  Figs.  257  to  262 .  137 

89.  Further  experiments.  8  =  10  cm.  8'  variable .  140 

90.  Pin-holes  varied.  Figs.  263  to  268 .  1 41 

Chapter  V — Miscellaneous  Experiments  with  the  Interferometer  U  gage 

91 .  Pressure  phenomena  of  the  electric  wind.  Apparatus .  146 

92.  Needle  electrode.  Figs.  269  and  270 .  146 

93.  Mucronate  electrode.  Figs.  271  to  275 .  148 

94.  The  same  with  micrometer.  Figs.  276  to  279 .  150 

95.  Contributory  results.  Figs.  280  to  282 .  1 5 1 

96.  Velocity  of  the  winds . 153 

97.  A  method  of  measuring  the  energy  of  X-rays.  Introductory  apparatus.  Fig.  283 .  .  154 

98.  Computation . 156 

99.  Data.  Figs.  284  and  285 .  157 

100.  Modified  U -gage.  Apparatus  and  results.  Figs.  286  to  288 .  157 


CHAPTER  I 


SHORT  AND  SLENDER  AIR-COLUMNS.  CIRCUITS  WITHOUT 

EXPLICIT  CAPACITY 

1.  Circuits — -In  my  earlier  papers  I  have  frequently  taken  up  this  investi¬ 
gation,  more  or  less  incidentally.  The  present  work  is  intended  to  be  more 
systematic.  All  measurements  of  nodal  pressure  indicated  by  the  pin-hole 
probe  are  made  with  the  U-tube  interferometer.  Antinodes  do  not  respond. 

The  trend  of  the  work  may  most  easily  be  shown  by  describing  the  suc¬ 
cessive  circuits  used  and  the  acoustic  effects  observed  with  each.  In  figure 
i a,  E  is  the  primary  electromotive  force  (one  or  two  storage-cells)  sending  a 
current  in  series  through  the  two  telephones  T  and  T'  and  the  resistance  R. 
This  current  is  periodically  broken  by  the  plate  commutator  B ,  rotated  at 
controllable  speed  by  a  small  motor  (not  shown).  In  this  way,  both  telephones 
give  out  the  same  note,  the  pitch  being  determined  by  the  angular  velocity 
of  B.  One  of  the  telephones,  Tf,  is  provided  with  a  switch,  5,  so  that  its 
current  may  be  reversed. 

The  two  telephones  are  connected  at  the  mouthpieces  by  the  tube  tt\ 
originally  15  cm.  long  (effectively)  and  1.5  cm.  in  diameter.  At  right  angles 
to  it  and  at  its  center,  the  two  pin-hole  probes  (salient  s  and  reentrant  r) 
are  inserted  and  5  is  joined  to  the  one  shank  of  the  interferometer  U-gage  by  a 
short  end  of  rubber  tubing.  All  joints  are  sealed  with  wax.  This  circuit 
(fig.  1 6),  in  series,  admits  of  the  more  useful  modification  (1  c)  with  the  tele¬ 
phone  circuits  in  parallel.  Additional  resistances,  inductances,  capacities, 
may  here  be  inserted  at  L. 

In  figure  2,  a  small  inductor  I  (about  0.5  henry  in  the  secondary)  has  been 
introduced,  cell  E  feeding  the  primary.  The  telephones  T  and  T '  are  now 
operated  by  the  induced  current  with  a  switch  at  5  for  one  of  them.  A 
resistance  at  R  is  convenient.  In  the  arrangement,  figure  3,  two  identical 
secondaries,  I  and  are  wound  side  by  side  on  the  same  primary,  the  other 
adjustments  remaining  as  before. 

In  figure  4,  the  primary  circuit  from  E  actuates  the  telephone  T  directly, 
whereas  the  secondary  circuit  at  I  with  a  switch,  S,  passes  through  the  tele¬ 
phone  V .  This  (series)  arrangement  has  been  improved  in  figure  5,  where  a 
branch  circuit  from  the  primary  passes  through  the  telephone  T.  The  advan¬ 
tage  of  this  is  the  easy  equalization  of  telephone-currents  by  a  resistance,  R , 
placed  in  either  circuit,  additional  inductance  being  added  at  L. 

2.  Table  of  inductances — -As  determined  by  conventional  methods,  the 
approximate  values  of  the  resistances  and  inductances  to  be  used  in  the  follow¬ 
ing  tests  are  summarized  in  table  1.  The  two  layers  of  the  inductor  are 
unfortunately  not  equally  efficient.  Though  they  were  usually  joined  in 


ACOUSTIC  EXPERIMENTS  WITH  THE  PIN-HOLE 


series  or  in  parallel,  there  are  a  number  of  cases  in  which  it  was  desirable  to 
use  them  independently  and  in  opposition.  At  high  values  of  L  the  method 
became  insensitive  and  the  data  are  probably  low.  The  coil  L2  was  probably 
defective.  The  table  refers  to  wire  or  laminated  cores.  In  the  experiments 
solid  cores  were  often  used  when  they  were  convenient,  as  it  was  the  object 
here  to  bring  out  the  character  of  the  acoustic  behavior  as  a  whole,  over  a 
wide  range.  Steps  of  increasing  inductance,  therefore,  are  frequently  useful. 
Large  continuous  changes  of  L  are  most  efficiently  made  by  inserting  a  core 

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e  g  a  c' ct ef  (£  a' ere  y  a  e/ cf  e' yalc'e  q  a  d  a' d  fy'a' e y  a  a  d!  e'  fyas d  e  $  a  ad! d q.'a' d  ot’ 


into  the  coil,  and  this  plan,  in  spite  of  its  deficiencies,  will  have  to  be  used 
below.  The  use  of  cored  coils,  otherwise  objectionable,  is  permissible  here, 
where  the  object  is  to  exhibit  the  acoustic  phenomena,  and  these  demand 
large  inductances. 


Table  i — ’Resistances  and  inductances  of  the  coils  used.  Conventional,  single  impulse 

methods.  All  coils  wire-cored 


Coil  No. 

R  ohms 

L  henry 

Coil  No. 

R  ohms 

L  henry 

Lx . 

u . 

l3 . 

lk . 

Inductor  second-//' 
aries . \7 

9-9 

301 

550 

1. 1 
30.5 
31-8 

O.32 

.13+ 

1-35+ 

.042 

•39 

.29 

Common  tele¬ 
phones  . 1 

Radio  tele-  1 

phones . 1 

Lw . 

M.  H.  standard . 

rr 

\T 

rr 

L  T 

84- 3 

85- 3 
iiio 

1090 

1. 1 

9-7 

0.060 

.060 

1.2 

1.2 

.Oil 

.010  to  .034 

3.  Survey  in  pitch — The  graphs  (figs.  6,  7,  8,  9,  10)  obtained  with  each 
of  the  circuit  designs,  showing  the  fringe  displacement  s  (nodal  intensity) 
as  the  pitch  gradually  rises  from  c  (4-foot  octave)  to  a'  (2 -foot  octave)  are 


PROBE  AND  THE  INTERFEROMETER  U-GAGE 


3 


given  below  the  corresponding  diagrams  of  circuits.  With  the  telephone- 
plates  in  phase  (i.  e.t  the  plates  moving  outward  or  inward  together)  there  is 
marked  response  (node)  between  a'  and  g'  and  again  between  a  and  g;  above 
a'  the  tube  is  silent  indefinitely.  Between  a'  and  a  there  is  here  apt  to  be 
multiresonance,  so  that  the  air-column  vibrates  at  all  pitch  intervals.  The 
saliency  at  a\  a,  though  usually  very  pronounced  (figs.  6,  7,  8),  is  sometimes 
reduced  as  in  figure  10,  n,  n possibly  owing  to  inherent  differences  of  phase 
in  the  two  circuits,  but  probably  incidental,  as  the  curves  m,  m'f  obtained 
with  somewhat  modified  telephones,  imply. 

When  the  current  in  the  telephone  Tr  is  reversed  by  the  switch  5,  the  plates 
vibrate  inward  and  outward,  respectively;  i.  e .,  in  sequence;  the  nodes  thus 
vanish  from  the  middle  of  the  tube  and  appear  at  the  ends.  There  is  there¬ 
fore  no  middle  pin-hole  pressure  (s)  at  pitches  a,  a'.  Curiously  enough,  there 
was  response  (middle  node)  in  this  case  at  e,  e'}  sometimes  quite  marked,  as 
in  figure  6,  but  usually  weak.  This  e  may  be  due  to  multiresonance,  as  the 
pipe  tt'  in  these  experiments  was  attached  to  the  telephones  by  short  quill- 
tubes.  One  would  therefore  expect  a  response  for  the  pipe  tt'  alone  and 
another  corresponding  to  the  added  space  around  the  telephone-plates,  a  sort 
of  Rayleigh  neck  effect.  It  was  subsequently  traced  to  an  inequality  in  the 
mouthpiece  of  the  telephones. 

If  but  one  of  the  telephones  is  actuated,  the  other  being  silent,  the  reso¬ 
nance  at  a  and  at  e'  were  sometimes  clearly  in  evidence,  as  in  figure  9.  When 
both  vibrate  in  phase,  however,  the  salient  e'  is  wiped  out  or  obscured.  Later 
the  e'  was  eliminated. 

4.  Continuous  change  of  phase  difference — This  is  most  easily  brought 
about  by  inserting  increasing  resistances  in  one  of  the  duplicate  telephone 
circuits,  leaving  the  other  unchanged.  The  first  test  was  made  with  the 
design  of  figure  3  and  the  results  are  shown  in  figure  11.  Between  o  and  1,000 
ohms,  the  fringe  displacements,  s,  are  given  in  steps  of  100  ohms;  between  1,000 
and  10,000  ohms,  in  steps  of  1,000  ohms.  The  phase  displacement  graph 
falls,  while  the  sequence  graph  rises  at  a  rapid  rate  continually.  From  the 
initial  difference  of  As  =  (87  —  3)  =84  at  R  =  o  to  the  final  difference  of  As  = 
60  —  60  =  0  at  R—  10,000  ohms,  the  curves  have  become  asymptotically  coin¬ 
cident.  The  fall  of  (middle)  nodal  intensity  from  5  =  87  to  5  =  60  is  due  to  the 
fact  that  in  the  latter  case  but  a  single  telephone-plate  vibrates,  whereas  the 
other  reflects  like  a  rigid  wall.  In  the  former  case  both  plates  vibrate,  rein¬ 
forcing  each  other.  The  As  curves  (fig.  11)  show  that  the  decrease  also  begins 
gradually,  as  though  some  inherent  phase-difference  were  first  to  be  compen¬ 
sated.  As  a  whole,  we  have  in  the  sequence  graph  an  interesting  exhibit  of  a 
continuous  change  of  the  type  of  reflection;  initially  without  change  of  phase, 
without  middle  node  (5  =  3)  it  passes  eventually  into  reflection  with  change  of 
phase  and  a  strong  middle  node  (s  =  6o).  The  lower  graph  offers  a  means  of 
converting  any  As  observed  into  the  corresponding  excess  resistance  R. 


4 


ACOUSTIC  EXPERIMENTS  WITH  THE  PIN-HOLE 


5.  Phase  difference  apparently  passing  through  zero — In  figure  n,  one 
telephone  is  silenced  before  appreciable  phase  reversal  occurs,  possibly  because 
the  initial  resistances,  etc.,  in  the  T  and  T'  circuits  (fig.  3)  are  large.  The 
trial  was  therefore  repeated  with  the  adjustment  figure  1  c,  and  an  example 
of  the  results  obtained  is  given  in  figures  12,  13,  and  14.  The  curves  now 
intersect  at  1,000  ohms  when  one  of  the  telephone-plates  is  effectively  at  rest. 
Thereafter  this  telephone,  as  it  were,  tends  to  vibrate  more  and  more  in 
phase  again;  but  the  relatively  high  resistances  soon  cut  the  modified  circuit 
out.  One  notes  that  the  sequence  curve  still  rises  with  increasing  resistance 
after  the  phase  graph  has  ceased  to  fall. 


Anticipating  the  results  below  (cf.  §  23),  if  we  suppose  a  telephone  to  be 
more  efficient  when  vibrating  under  phase  conditions  (or  the  reverse)  than 
under  sequence  conditions,  and  introduce  to  constants  c  and  c'  to  allow  for 
this  difference,  we  may  picture  the  case  of  intersecting  or  nonintersecting 
phase-sequence  graphs  perhaps  as  follows:  Since  the  circuits  T,  Tf  in  the 
adjustment  in  figure  1  c  are  in  parallel,  and  if  As  is  the  fringe  displacement  in 
the  sequence  case  and  Us  in  the  phase  case, 

(1)  As  =  f  { i/c  V  R*  +  LW  -  1  /c'V  R?  +  LV } 

(2)  2s  =  e  { i/c  Vr „2  +  LV  +  i/c  Vr }  +  LV } 

where  Rv  is  the  varied  and  Rc  the  constant  resistance  of  the  telephone-circuits, 
L  their  (identical)  inductance,  €  the  e.  m.  f.  in  proper  units.  Now,  if  Rv  =  00 , 
apart  from  signs 

(3) 


—  A  s/Hs  —  c/cr 


PROBE  AND  THE  INTERFEROMETER  U-GAGE 


5 


i.  c.}  they  are  unequal.  If,  however, 

(4)  As  =  e  { I  /c  Vr*  +  LV  - 1  /c'  Vr*  +  LW } 
i.  e.,  if  the  varying  resistance  is  in  the  other  circuit,  then,  if, 

(5)  Rv=  co  As/Hs  =  c/c  =  1 

In  the  case  (3),  if  c'  >  c,  the  phase-sequence  graphs  would  eventually  intersect; 
whereas  in  the  case  (5)  they  would  meet  at  Rv  =  co .  The  results  would  be  the 
same  if  in  equation  (2)  the  constant  were  c\  the  argument  being  that  if  both 
telephones  vibrate  in  phase,  i.  e .,  alike,  they  are  equally  efficient,  but  not  so 
in  the  opposite  case.  Both  cases  occur  in  the  present  experiments. 

Equation  (3)  and  figure  14,  then,  give  us  the  ratio  of  telephone  efficiency, 
c/c' =  40/34  =  1. 18,  a  value  which  reappears  below,  §  23. 


6.  Phase  reversal  owing  to  inductance — After  this  a  large  number  of 
experiments  were  made  with  capacities  ( C )  and  inductances  (L)  with  the  hope 
of  observing  more  striking  phase  reversals,  but  at  first  without  much  success. 


I  give  a  few  examples  in  figure  15,  the  empty  coils  being  first  inserted  into  one 
telephone-circuit  ( T',  fig.  3)  and  the  iron  core  thereafter.  The  steps  of 
inductance  L  may  be  estimated  as  within  one  henry  (cf.  §  12),  though  they 
were  not  nearly  so  large  at  the  frequency  a'  (440),  since  the  cores  of  iron  were 
not  laminated.  The  survey  in  pitch  carried  out  in  the  graph  at  each  L  is  in 
conformity  with  the  unloaded  graph. 

Figure  16  is  a  summarized  example  of  the  fringe  displacements  5  found 
(adjustment,  fig.  ic)  after  the  inserting  of  the  coils  (resistance  R)  and  after 
the  subsequent  insertion  of  the  iron  cores  (Li,  L2,  L3).  In  these  cases  the 
phase  curve  tends  to  become  horizontal,  while  (after  the  intersection)  the 
sequence  curve  still  rises  in  marked  degree.  Hence  the  explanation  of  the 
apparent  L-effect  is  probably  the  same  as  that  in  the  preceding  section. 

An  interesting  result  was  obtained  in  comparing  hollow  and  solid  iron 
cores.  The  L-efTect  in  the  two  cases  was  about  the  same.  Thus,  in  inserting 
an  inch  solid  rod  into  the  coil  L2,  the  As  observed  with  and  without  iron  was 
not  appreciably  larger  than  when  the  same  length  of  inch  gas-pipe  was  inserted. 
Thus  the  iron  at  frequencies  above  400  per  second  here  exhibits  an  astonishing 
magnetic  skin  or  shielding  effect. 


6 


ACOUSTIC  EXPERIMENTS  WITH  THE  PIN-HOLE 


To  give  two  examples  (fig.  17)  among  many  for  coil  II,  when  a  tin-plate 
tube,  inch  gas-pipe,  and  solid  inch  rod  were  used  as  cores  successively : 

Full  displacement .  As  =  1 10,  72  Coil  with  gas-pipe  core .  As  =  2 1 ,  16 

Coil  in  (without  iron) . As=  35,  25  Coil  with  solid  core .  As  =  21,  16 

Coil  with  shell  core . As=  23,16 

7.  Data — Treating  the  fringe  displacements  As  as  equivalent  to  the  effec¬ 
tive  or  virtual  current  in  the  telephone,  a  few  tentative  tests  were  begun,  using 
the  graphs,  figure  12,  for  converting  s  into  the  excess  resistance  R  in  circuit, 
E ,  R,  L,  C ,  w  having  their  usual  meaning.  Hence  if  we  temporarily  disregard, 
as  both  figures  11  and  12  seem  to  permit,  the  inherent  phase  differences,  the 

telephone  amplitude  may  be  written  E/^R2  +  (i/Cco  — Leo)2,  E  being  the  volt¬ 
age  applied  and  R  (allowing  for  the  telephone  resistance)  following  from  As 
in  figure  12. 

If,  therefore,  the  same  reduction  of  As  is  produced  in  one  case  by  addi¬ 
tional  resistance  (coils  only)  and  in  the  other  by  additional  inductance  (iron 
core  in)  from  the  same  initial  As,  we  may  write 

E/VR '2  +  (i/Cco— jLco)2  —  E/VR "2  +  (1  /Cco-Ico)2  = 

E/Vr '2  +  (i/Cco-ImY-  E/Vr'2  +  (i/Cco-L'co)2 

whence  on  inverting  the  squared  quantity, 

( Lco-i/Ca))2-(L'w-i/Cu >)2  =  R"2—R'2  =  A  R2 
or, 

c c(L  -f-  L ')  —  2/Cco  =  AR2/uAL 

where  A L—  L—L’  is  negative.  For  another  coil,  Li,  Ri,  of  the  same  C  and  w, 

co(Li  T"  E'i)  —  2C00  ==  ARi2 / ooALi 

whence 

CO 2  { (L,  +  L\)  ~  (L  +  L') }  =  Ai?i2/AL,  -  &R2/AL. 

If,  therefore,  it  were  permissible  to  neglect  the  initial  inductance  (L  = 
L'  =  o)  of  the  coils,  without  iron,  observing  that  A L  and  ALi  are  positive  if  the 
squares  above  are  not  inverted 

(1)  ±coL'i  +  ARi2/ccL\  =  ±coL'  +  A  R2/o)L'  =  K  =  const. 

Thus,  if  K  is  known,  from  L'  as  a  standard 

(2)  L'i  =  ±  (K/ 2io)  (1  +  Vx  i  4A W/K*) 

If  capacity  (C)  is  excluded,  the  equations  under  the  same  limitations  are 
much  simpler  and  become 

Vl2-L02  =  VlV-Rf/u 

where  L0  and  R0  refer  to  the  initial  circuit  and  L  and  R  to  the  circuit  after  the 
coil  is  inserted. 


PROBE  AND  THE  INTERFEROMETER  U-GAGE 


7 


The  following  data  were  obtained  by  the  method  of  figure  i c,  the  full 
fringe  displacement  in  the  absence  of  coils  being  As  =  65. 

The  coils  I,  II,  III,  IV  (cf.  §  2)  were  of  the  choke-coil  type,  with  removable 
iron,  except  the  last  two,  V,  VI,  where  the  iron  was  fixed.  These  were  parts 
of  a  little  induction  coil  consisting  of  two  half  secondaries.  They  behaved  so 
peculiarly  that  the  full  data  are  noteworthy  (cf.  fig.  18). 


Coil  out 

Layers  in 
parallel 

Layers  in 
series 

One  layer 
only,  V 

The  other 
layer,  VI 

In  phase  y . 

75 

65 

65 

65 

65 

In  sequence  5 . 

3 

23 

37 

42 

40 

As . 

72 

42 

28 

23 

25 

So  far  as  the  phase  graph  is  concerned  it  makes  little  difference  how  the 
layers  are  taken.  The  sequence  graph  rises  naturally  when  the  two  layers  are 
combined  in  parallel  and  then  in  series;  but  curiously  enough,  each  single 
layer  shows  greater  impedence  alone  than  when  they  are  taken  together  in 
series.  These  apparently  anomalous  results  remained  the  same  throughout 
many  repetitions.  The  impedence  of  the  half  coil  (caet.  par.)  behaves  as 
if  it  were  greater  than  the  whole.  One  suspects  the  occurrence  of  electric 
oscillation. 


Table  2 — Initial  As  =  65,  equivalent  to  R  =  100  ohms  and  L0.  (L2— Z,02)  oc  (R2  — R^/w1. 

Frequency,  n—  440,  co=  2765. 


Coil  No. 

I 

II* 

III 

IV 

Coil  No. 

I 

II 

III 

IV 

As  (no  core) . 

As  (iron  core) . 

R  (no  core) . 

R  (iron  core) . 

A R  (core-coil) . 

45 

19 

60 

225 

165 

10 

5 

370 

5io 

140 

8 

3 

420 

620 

200 

54 

28 

30 

150 

120 

(. Rd2-Ro 2)  X  ro-q 
(. Rco2-Ro 2)  x  io-q 

Lcl  (henry)  f . 

Lcore  (henry) X  ... . 

Total  (henry) .  . 

0.156 

•956 

•045 

.112 

2. 11 
3.62 

•  •  • 

•  •  • 

2.60 

5.08 

.185 

.258 

0.169 

•525 

.030 

.083 

•157 

•443 

.  .  . 

*  Defective  coil. 

t  Corrected  for  telephone  resistance  (ioo  ohms). 
X  Interpolation  Lobs  ~  0.090  -f  0.25  L. 


In  table  2  the  values  of  A 5  and  their  reductions  to  resistance  R  (fig.  12) 
are  given,  together  with  the  tentative  values  (nearly)  computed  from  them. 
The  difference  between  the  L  with  and  without  solid  iron  cores  is  astonishingly 
small,  relatively  speaking.  The  data  as  a  whole,  compared  with  table  1, 
give  a  crude  order  of  values  only.  The  coil  L2  was  subsequently  found  to  be 
defective.  Omitting  this,  the  other  values  of  total  L  observed  here  and  the 
data  of  table  1  (L)  conform  pretty  closely  to  the  equation 

Lobs  =0.090  +  0.25  L 

Thus  at  L=i  henry  Lobs  =0.34.  The  constant  indicates  that  the  postulates 
are  not  admissible. 


8 


ACOUSTIC  EXPERIMENTS  WITH  THE  PIN-HOLE 


8.  The  equations  completed.  Single  circuit — Assuming  that  the  current 
in  T  remains  practically  constant  in  the  current  designs  (figs.  3,  5)  adopted, 
the  problem  is  reduced  to  the  variations  of  the  current  I,  subject  to  L,  R,  co 
in  the  telephone  T'.  This  is  to  pass  to  I'  when  L,  R  is  replaced  by  L,  R'y  and 
to  I"  when  the  former  is  replaced  by  L',  R.  These  changes  involve  three 

phases,  0  =  tan-1  Lcc/R,  0'  =  tan_1Lco/A',  and  0"  =  toxC1  L'oi/R. 

The  relations  here  in  question  are  given  in  the  usual  way  in  the  diagram 
(fig.  24),  with  the  value  of  all  the  vectors  and  angles  indicated.  C'  is  the 
circular  locus  on  the  diameter  E/Lu,  when  R  only  varies  (increase  counter¬ 
clockwise)  and  C"  the  circular  locus  on  the  diameter  E/R  when  L  (increase 
clockwise)  only  varies.  As  the  currents  I  were  identical,  the  projections  of  I ' 
and  I"  on  I  must  be  the  same,  as  they  produce  the  same  depression  in  the 

As  graph.  Hence 

I'  cos  (0-0')  =  I"cos  (0"-0) 
or 

(1)  E  cos  (6-0')/ V R '2  +  LW  =  E  cos  (0" - 0)/  V R2  +  Z/ V 
If  we  put  0  =  cos  (0*  —  0)/  cos  (6—6')  the  former  equation  reduces  to 

(2)  co2  (Z/2- 02L2)  =  G2R'2  —R2 

thus,  if  0  =  1,  the  old  equation  would  follow. 

To  find  0,  the  equations  0  =  taxT1  Lai/R,  etc.,  may  be  reduced  and  the 
result  is 

(3)  02  =  (i/LV  +  i/R'2)/(i  /L'V  +  1  /R2) 

If  this  value  is  introduced  into  equation  (2),  the  latter  expressed  for  L'2—L2 
gives 

(4)  co2  (L'2  -  R2L2/R'2)  =  (R2/LW)  (R'2  -  L2R2/L'2) 

If  R  and  L  are  small,  the  coefficient  of  the  last  L2  and  R2  may  be  disregarded; 
but  the  approximate  result 

(5)  a>2AL2  =  (R2/LW)  A R2 
is  still  essentially  dependent  on  (R/Loi)2. 

9.  Circuits  in  phase  and  in  sequence — The  simple  premises  of  the  pre¬ 
ceding  paragraph  are  inadequate.  Each  point  in  the  diagram  involves  two 
circuits  in  parallel.  If  we  proceed  as  in  §  23  below,  letting  the  constants  c ,  c' 
refer  to  the  efficiency  of  the  telephones  and  suppose  the  electromotive  force 
8  in  proper  units,  a  point  in  the  phase-graph  is  equivalent  to 

s  =  s  (1  /c  V Rc 2  +  L0n  0>2  +  i/c  Vrv 2  +  L}  a2) 

when  Rv  and  Rc  are  the  varied  and  the  constant  resistance.  A  point  on  the 
corresponding  sequence-graph,  however,  is  equivalent  to 


s  =  s  (i/c  Vr*  +  L0 V - 1  /c'  VR*  +  Z.„V) 


PROBE  AND  THE  INTERFEROMETER  U-GAGE 


9 


c  and  c'  occurring  here,  because  the  telephone-plates  vibrate  in  opposed 
phases.  The  constants  c  and  c’  may  be  exchanged.  Hence  the  initial  As 
has  the  form :  _  _ 

As  =  e  { i/c  VR „2  +  L„V  +  i/c’  Vr)  +  L„V  } 

If  the  effect  of  adding  R  is  identical  to  the  effect  of  adding  L,  the  new  As'  reads 

As'  =  s{  i/c  V(R,  +  R)*  +  +  i/c'  V(Rv  +  R)2  +  L„V }  = 

e  { i/c  Vr)  +  (L„  +  L) V  +  i/c’  Vr*  +  (L.  +  L) V } 

Hence  it  is  the  difference  of  c  and  c'  which  complicates  this  equation.  If  c  =  c' 
the  last  equation  reduces  to 

AR2  =  gj2AL2 

giving  the  approximate  values  of  table  2 . 

10.  Improvement  of  telephones — Before  beginning  the  next  series  of 
observations,  the  telephones  were  overhauled  as  to  tightness,  etc.  Some  change 
seems  thus  to  have  been  made  in  the  space  within  the  mouthpiece.  For  after 
a  survey  in  pitch  the  graphs  like  figure  19  appeared.  In  the  resulting  phase- 
curve  there  is  a  closer  approach  to  silence  between  a'  and  a.  In  the  sequence 
curve  the  maxima  at  e't  e,  have  vanished.  They  were  thus  probably  due  to 
unequal  spaces  ahead  of  the  plates,  or  to  some  similar  effect.  The  present 
sequence  curve  now  also  has  small  maxima  at  a!  and  a,  which  being  due  to 
inherent  differences,  now  becomes  important.  The  new  adjustments  wrere  used 
to  try  out  the  inductance  of  coil  II  again,  with  a  core  of  cylindrical  iron,  shell 
of  gas-pipe,  and  a  solid  core  respectively.  The  data  (fig.  20),  given  as  hereto¬ 
fore,  corroborate  the  old  results.  The  cylindrical  shell  is  nearly  as  effective  in 
L  as  the  inch  solid-iron  core. 

11.  Comparison  of  primary  and  secondary — The  design  here  used  is 
again  the  circuit  shown  in  figure  5.  The  effect  of  resistances  in  the  primary  is 
given  in  figure  21,  both  in  steps  of  100  ohms  and  of  1,000  ohms.  It  contains 
nothing  unexpected.  The  circuit  resistances  being  small  and  the  inherent 
phases  favorable,  additional  resistances  (2,000  ohms)  soon  practically  quench 
vibration  in  the  loaded  circuit.  The  initial  and  final  nodal  intensities  5  for  the 
phase-curve  are  as  100  : 75.  Here,  however,  a  new  feature  enters,  since  the 
sequence  curve  begins  with  an  intensity  of  5  =  27.  The  phase-sequence 
graphs  do  not  cross. 

Similar  results  are  summarized  in  figure  22  (attached  to  figure  14)  for 
successive  loads  of  self-induction  in  the  primary,  L  referring,  as  stated,  to 
the  coils  either  alone  or  with  iron  cores.  These  curves  (phase  and  sequence) 
could  be  made  to  just  cross  by  inserting  more  inductance.  The  sequence 
curve  again  begins  with  large  s,  to  be  associated  with  a  lag  in  the  primary 
or  a  lead  in  the  secondary,  since  the  added  L  increases  s. 

The  effect  of  additional  resistance,  R,  in  the  secondary  shown  in  figure  23, 


10 


ACOUSTIC  EXPERIMENTS  WITH  THE  PIN-HOLE 


is  also  normal  in  character.  The  phase  and  sequence  curves  gradually  approach 
each  other  and  coincide  when  R  =  10,000  ohms;  but  they  do  not  cross.  Neither 
does  the  initial  progress  ( R  =  o)  suggest  any  novelty. 

In  figure  2  7 ,  however,  which  indicates  the  effect  of  inserting  self-induction 
in  steps  in  the  secondary,  there  is  an  interesting  new  departure  at  the  begin¬ 
ning.  The  phase  and  sequence  graphs  no  longer  finally  cross  each  other,  but  the 
sequence  graph  at  first  actually  descends,  showing  probably  that  the  opposi¬ 
tion  in  phase  is  made  more  perfect;  i.  e.,  a  lead  compensated  by  an  increasing 
lag,  resulting  from  the  initial  insertion  of  inductance.  No  such  effect  was  here¬ 
tofore  produced  with  initial  resistances  (fig.  23)  either  in  the  primary  or 


secondary.  Thus  for  the  first  time  we  encounter  an  inherent  phase  difference 
equivalent  to  6  =tan-ILa> /R.  The  L  experiments  were  frequently  repeated  to 
test  their  consistency,  and  a  good  example  is  given  in  figure  28  for  inductance 
and  figure  26  for  resistance,  for  a  somewhat  larger  impressed  e.m.f.  If  we 
regard  the  phase  difference  of  primary  and  secondary  as  an  advance  of  the 
secondary,  the  insertion  of  inductance  at  first  seems  to  retard  it  into  complete 
opposition  (sequence)  with  a  maximum,  after  which,  with  further  inductance, 
the  opposition  passes  more  and  more  fully,  evoking  the  middle  node  more  and 
more  clearly.  The  graphs,  figures  27  and  28,  have  therefore  been  drawn  in 
full  through  the  data  as  obtained;  but  a  suggestion  of  the  probable  course 
presently  to  be  verified  is  given  by  the  broken  lines  in  figure  28.  If  phase 
reversal  is  interpreted  as  a  negative,  s,  the  regularity  of  curves  is  everywhere 
enhanced.  It  appears  also  that  whenever  such  reversal  occurs,  the  cause 


PROBE  AND  THE  INTERFEROMETER  U-GAGE 


11 


of  the  production  of  the  middle  node  passes  from  one  telephone  to  the  other. 
In  the  dotted  sequence  curve,  if  the  telephone  T  is  heard  below  the  abscissa, 
the  telephone  T'  will  be  heard  above  it. 

Further  detail,  obtained  with  the  same  adjustment  later,  is  given  in 
figures  29  and  30,  where  the  resistances  in  the  former  figure  evoke  the  same 
march  of  5-values  without  minima  in  the  sequence  graphs.  Figure  30,  in 
which  the  inductions  La  are  given  by  a  long  choke-coil,  the  iron  core  of  which 
could  gradually  be  thrust  in  to  the  extent  indicated  in  the  curves,  shows  the 


sequence  minimum  more  closely.  It  may  possibly  have  fallen  to  5  =  0  in  the 
lower  graph,  as  no  inductances  between  La  and  L2+L4  were  available,  and  the 
latter  carries  the  observations  beyond  the  minimum.  The  curves  a,  b  were 
obtained  without  excess  resistance  ( R  —  o )  in  the  T'  circuit,  the  curve  c  d, 
however,  with  an  excess  resistance  of  R  =  500  ohms.  The  original  minimum 
has  flattened  out,  since  L  is  now  relatively  inefficient.  At  R  =  1,000  ohms  in 
the  T'  circuit,  the  effect  of  the  inductances  used  is  negligible. 

12.  Layers  of  transformer  in  parallel — After  these  results  it  seemed 
obvious  that  a  greater  initial  current  for  the  sequence  graph  would  appear  on 
reducing  the  impedance  of  the  secondary  of  T'  by  putting  the  two  identical 


12 


ACOUSTIC  EXPERIMENTS  WITH  THE  PIN-HOLE 


layers  (fig.  5 ;  compare  fig.  3)  in  parallel.  The  telephone  T  is  of  course  left  in 
the  primary.  This  surmise  is  borne  out  in  figure  31,  where  the  fringe  dis¬ 
placements  5  are  given  in  terms  of  the  inductance  L,  increasing  in  steps.  The 
experimental  As  curve  here  shows  a  well-marked  maximum,  while  the  sequence 
curve  passes  sharply  through  a  minimum.  By  gradually  inserting  the  iron 
core  into  the  coil  L3,  it  was  possible  to  trace  these  curves  continuously;  but 
unfortunately  the  minimum  s  =  io  was  reached  when  the  core  was  quite  in. 
It  is  clear,  however,  that  the  sequence  graph  must  actually  fall  to  the  abscissa 
and  the  curve  is  drawn  to  correspond  with  its  resonance  location.  The  graphs 
in  figure  31  are  thus  an  enlargement  of  figure  28  in  sensitiveness  and  are  at 
the  same  time  pushed  to  the  right,  revealing  new  contours  on  the  left. 

If  one  again  considers  the  descending  branch  of  the  sequence  curve 
negative  in  phase,  the  ascending  branch  positive,  as  suggested  by  the  dotted 
line,  the  doubly  inflected  curve  resulting  may  be  regarded  as  a  better  picture 


of  the  phenomenon,  as  a  whole.  At  5  =  0,  the  sound  passes  from  one  tele¬ 
phone  to  the  other.  Apart  from  the  ends,  the  main  run  of  the  graph  is  now 
nearly  straight.  The  same  is  true  of  the  As  graph  if  the  ascending  parts  of  the 
sequence  graph  are  regarded  negative  in  phase  and  therefore  to  be  added  to 
the  phase-graph.  The  As  line  is  then  surprisingly  uniform  in  character,  with 
the  characteristic  double  inflection. 

The  interesting  results  in  figure  31  deserve  further  elucidation,  to  be 
obtained  by  changing  the  resistance  of  the  T'  circuit  simultaneously.  Figure 
32  gives  a  case  of  the  kind,  where  R  only  is  increased  (in  steps  of  100  ohms  and 
of  1,000  ohms  as  stated),  without  addition  of  L  to  the  T'  circuit.  The  feature 
of  the  diagram  is  again  the  minimum  at  about  200  ohms  in  the  sequence-graph. 

Figure  33  (equivalent  to  figure  31  but  obtained  under  different  L  con¬ 
ditions)  shows  the  corresponding  effect  of  inductances,  increased  continuously 
by  inserting  the  core  into  the  L\  coil  in  thirds  of  its  length.  The  sequence- 
graph  runs  through  s  —  o,  as  before. 

In  figure  32,  the  additional  branches  a  and  b  indicated  that  when  the  same 
increments  of  L  are  applied  when  R  =  500  ohms,  there  is  little  appreciable 


PROBE  AND  THE  INTERFEROMETER  U-GAGE 


13 


reduction  of  5  and  that  L  becomes  effective  only  when  it  is  relatively  large 
in  value  (L2  L\) . 

In  figure  34,  the  R-e ffect  is  investigated,  beginning  with  the  additional 
inductance  of  the  cored  L\  coil,  in  the  T'  circuit.  Naturally  the  5- values, 
as  a  whole,  are  reduced  and  the  R  minimum  of  the  sequence  curve  now  actually 
falls  to  zero  at  R  =  100  ohms.  The  sequence-graph  has  been  depressed  and  the 
minimum  moved  nearer  the  origin,  whereas  for  high  resistances  the  graph 
asymptotically  reaches  the  preceding  graph  (fig.  32)  for  L  —  o. 

In  figure  35,  R  is  increased  in  steps,  beginning  with  an  inductance  smaller 
(coil  La  with  core  two-thirds  inch;  curves  a,  b)  and  larger  (coils  L 2  and  La,  not 
cored,  curves  c,  d,  e ,  /),  respectively  than  observed  in  figure  34,  in  which  the 


origin  is  near  the  sequence  minimum.  Again  the  latter  has  been  moved  to 
the  right  and  raised  (curves  a,  b) ;  or  moved  to  the  left  beyond  the  coordinates 
(curves  c ,  d,  e,  /)  consistently  with  the  preceding  results. 

Finally  figure  36  gives  the  corresponding  results  when  L2  and  L\  (both 
cored)  are  inserted  in  the  Tf  circuit.  The  coordinates,  as  it  were,  are  further 
displaced  to  the  right  in  the  same  sense  as  in  figure  35. 

To  summarize  the  cases,  therefore:  it  is  found  that  the  5  minimum  of  the 
sequence-graph  moves  into  smaller  R  and  5  toward  the  origin,  when  L  is  suc¬ 
cessively  increased  until  the  minimum  vanishes.  Thereafter  the  sequence 
graphs  (without  the  minimum)  rise  again  as  L  increases  further;  but  this  may 
in  part  be  due  to  the  R- values  of  the  new  coils  added  in  the  later  stages.  The 
increased  difficulty  not  only  of  obtaining  an  5  minimum  in  the  sequence  graph 
(compared  with  the  preceding  case  of  L  variation),  but  of  bringing  this  mini- 


14 


ACOUSTIC  EXPERIMENTS  WITH  THE  PIN-HOLE 


mum  down  to  s  =  o  when  R  is  the  variable,  deserves  notice.  The  next  para¬ 
graph  is  a  correlative  illustration. 


13.  Single  half  layer — Using  but  one  of  the  identical  layers  of  the  inductor 
I,  figure  5,  fringe  displacements  indicating  the  intensity  of  the  middle  node 
were  obtained  as  summarized  in  figure  37.  This  is  virtually  a  return  to  figure 
28  for  the  series  experiment,  except  that  the  nodal  intensities  are  larger 
throughout.  The  decreased  impedence  is  an  advantage;  but  the  high  initial 
intensity  of  the  sequence  curve  of  figure  3 1  has  been  lost  because  of  the  double 
resistance  at  the  beginning.  By  continuously  inserting  the  iron  cores,  it  was 
here  possible  to  bring  the  sequence  curve  actually  to  and  through  5  =  0,  from 
which  it  follows  that  this  must  also  have  been  the  case  in  the  preceding  figures 
27,  28,  31,  where  the  relevant  data  are  incomplete.  The  dotted  curves  indicate 
the  passage  through  zero,  where  the  phase  opposition  would  be  complete,  when 
descending  sequence  branches  are  treated  as  negative  in  phase.  They  closely 
resemble  figure  31,  so  that  the  remarks  already  made  apply. 


14.  Incidental  origin  of  initial  phase  differences — If  the  telephone-plates 
are  exactly  in  opposed  phases,  the  sequence-graphs  should  begin  at  the  origin. 
This  is  very  rarely  the  case.  In  the  circuit-figure  5,  the  initial  phase  differ¬ 
ences  might  be  referred  to  the  comparison  made  of  primary  and  secondary; 
but  in  circuit  figure  3,  both  telephone  circuits  are  secondaries  excited  under 
apparently  like  conditions.  Nevertheless,  the  sequence-graph  begins  much 
above  5  =  0.  Thus  the  inherent  phase  differences  in  large  part  are  referable 
to  differences  in  the  induction  coils. 

To  test  this  preliminarily,  the  secondary  circuits  (fig.  3)  were  combined 
differentially,  by  joining  the  telephone  leads  to  the  points  and  3,  2,  and  4  re¬ 
spectively,  so  that  the  induced  currents  traverse  the  telephones  in  opposite 
directions.  The  residual  fringe  displacements  obtained  were  quite  marked; 
yiz, 

First  switch  position,  s  =  35  (Increased  primary  current)  5  =  55 
Second  switch  position,  s'  =23  s'  =  40 


Thus  it  follows  that  the  two  secondaries  I  and  I'  in  figure  2  are  not  equal, 
for  neither  5  nor  5'  are  zero,  and  that  the  telephones  are  not  equally  efficient 
in  case  of  a  reversal  of  current,  since  s'  >s. 

Moreover,  in  total  strength,  circuits  figure  2  and  figure  5  do  not  differ 
much;  viz, 


No.  3 


ph.  140 
seq.  33 


As  =  107 


No.  5 

(in  series) 


ph.  140 
seq.  30 


As  =  110 


No.  5 

(in  parallel) 


ph.  140 
seq.  60 


|  As  =  80 


To  throw  further  light  on  the  question,  experiments  were  made  with  the 
arrangement  of  figure  3,  by  putting  resistance  R  first  in  the  secondary  I 
and  telephone  T  and  thereafter  into  the  secondary  I'  and  telephone  T'.  The 
results  are  given  in  figures  38  and  39  with  the  resistances  in  steps  of  100  and 
of  i.ooo  ohms,  as  indicated,  the  fringe  displacements  5  being  mapped  for  each 


PROBE  AND  THE  INTERFEROMETER  U-GAGE 


15 


case.  The  results  are  very  different.  As  a  whole  the  5-values  of  figure  39 
lie  much  above  those  of  figure  38,  showing  greater  impedance  (probably 
largely  resistance)  in  the  latter  case,  viz, 


Telephone  T 

Telephone  T’ 

Initially 

Finally 

Initially 

Finally 

Phase . 

I40 

95 

I40 

Il6 

Sequence.  . 

28 

93 

37 

120 

As . 

1 12 

2 

103 

-4 

so  that  the  latter  curves  cross  as  in  the  above  figures  12,  13,  14.  Again, 
while  the  phase-graph  for  T  falls  more  rapidly  than  for  T',  the  sequence 


graph  of  T  rises  more  slowly  than  for  T\  both  of  which  culminate  in  the  differ¬ 
ent  5-levels,  at  the  end,  when  one  telephone  is  apparently  silent.  Finally,  the 
insertion  of  resistances  into  T  actually  reduces  the  initial  5-values,  which  pass 
through  a  minimum  5  but  never  approach  5  =  0  (seq.  graph,  fig.  38).  As  a 
whole,  therefore,  the  behavior  (figs.  38  and  39)  is  very  much  as  if  IT  were  an 
outer  coil  of  smaller  inductance  and  larger  resistance,  I'T'  an  inner  coil  of 
larger  inductance  and  smaller  resistance,  wound  about  the  same  primary. 
The  minimum  sequence  5  of  figure  38  will  have  to  be  referred  to  changes  of 
phase  due  to  R,  since  the  current  and  phase  difference  (tan-1  Lu/R)  both 
decrease  with  R. 

To  bring  the  minimum  of  figure  38  quite  to  zero  is  accomplished  by 
inserting  additional  inductances  L,  continuously.  I  again  used  the  choke- 
coil  L4,  as  above,  and  figures  40  and  41  show  the  results  when  the  iron  core  is 
gradually  pushed  in.  The  abscissa  is  just  reached  in  figure  38  (so  that  this 


16 


ACOUSTIC  EXPERIMENTS  WITH  THE  PIN-HOLE 


graph  is  ahead  of  the  minimum)  and  with  larger  inductances,  the  curve  would 
rise  again  as  heretofore  (figs.  31,  37).  Figure  39  is  beyond  the  minimum  and 
s  increases  continually  in  the  sequence  graph  while  the  telephone  T'  is  being 
hushed. 

It  follows,  therefore,  that  the  method,  figure  3,  unless  the  coils  have  been 
specially  wound,  complicates  the  interpretation  of  results.  These  difficulties 
vanish  in  case  of  such  methods  as  in  figure  25,  particularly  when  the  two 
half-coils,  if  used,  are  joined  in  parallel.  It  is  thus  clear  that  in  the  latter 
cases  the  assumption  of  a  phase  difference  between  primary  and  secondary 
due  to  R ,  L,  C  is  trustworthy. 

The  insertion  of  induction,  after  the  sequence-graph  (cf.  fig.  40)  has  been 
raised  by  resistance,  merely  diminished  the  L-effect  for  R  —  o.  Thus  at  R  =  400 
ohms  in  figure  40,  the  graph  drops  from  5  =  35  to  5  =  26  for  the  full-cored  L4  coil 


pretty  uniformly.  At  R  =  600  ohms  the  fall  of  5  is  but  two  or  three  scale- 
parts,  so  that  the  L-effect  is  nearly  negligible. 

One  may  notice  that  whereas  in  figure  39  the  phase-sequence  graphs 
intersect,  this  is  not  the  case  in  figure  38.  Thus  these  observations  agree  with 
the  explanation  given  in  §  6. 

15.  Circuits  without  transformer — The  design  of  figures  3  and  5  have 
the  advantage  for  the  present  purposes  of  admitting  large  initial  or  inherent 
phase  differences,  equivalent  to  a  lead  in  the  telephone  T'  to  be  loaded.  This  is 
not  at  once  the  case  with  circuits  of  the  type  figure  1  c\  but  these  circuits,  being 
simpler,  are  in  a  measure  better  adapted  for  computation.  There  is,  however, 
liable  to  be  some  small  inductive  difference  or  its  equivalent  in  the  telephones, 
as  shown  in  figures  42,  43,  with  the  adjustment  in  parallel  given  in  the  inset, 
figure  42,  B  being  the  break.  The  effect  of  resistance  is  the  usual  fall  of  phase- 
graph  and  rise  of  sequence-graph,  with  some  hesitation  of  the  latter  at  the 
beginning.  Figure  43,  however,  shows  a  small  initial  lead  of  the  T'  circuit, 
which  could  be  wholly  wiped  out  by  gradually  inserting  the  iron  core  of  the 
L4  coil  as  the  sequence  graph  indicates.  The  lag  of  T'  does  not  appear  until 
after  the  whole  of  the  Li  core  is  thrust  within  the  coil.  The  further  inductance 


PROBE  AND  THE  INTERFEROMETER  U-GAGE 


17 


L2  acts  in  part  through  its  coil  resistance,  which  can  not  here  be  excluded, 
so  that  a  broken  curve  results.  The  phase-graph  is  almost  stationary  with 
L4,  but  drops  rapidly  with  L2+L4.  If  the  design  (insert,  fig.  42)  is  adjusted 
in  series  (insert,  fig.  44),  the  current  in  the  single  circuit  merely  drops  off,  both 
with  increasing  R  and  L,  as  shown  in  figure  44.  Both  telephones  cease  to 
respond  on  loading,  together.  R  is  particularly  effective. 

16.  Telephone-plate  subject  to  an  external  magnetic  field — The  question 
occurred  whether  in  case  of  the  adjustment  (fig.  42,  insert),  it  would  be 
possible  to  produce  a  lead  in  T'  by  external  magnetic  attraction.  In  figure 
45,  T  shows  the  mouthpiece  of  the  telephone,  the  bent  magnet  M  being 
placed  as  near  as  possible  to  it,  straddling  the  acoustic  pipe  t.  The  results 
given  by  the  graphs  in  figure  45  are  very  definite.  The  vibration  in  phase  is 
much  diminished  in  strength,  but  is  not  otherwise  abnormal.  The  sequence 
graph,  below,  is  peculiar.  The  former  lead  at  the  beginning  (field  off) 


passing  through  zero  with  increased  inductance,  has  practically  vanished. 
Instead,  the  curve  now  rises  continually  and  the  divergence  of  curves  is  most 
marked  when  the  sequence-graph,  in  the  absence  of  field,  is  at  zero.  This 
implies  that  the  sequence  vibration  is  also  less  intense,  so  that  the  graph  as  a 
whole  rises  higher  throughout  when  the  field  is  on.  If  the  lead  in  the  sequence- 
graph  (field  off)  is  plotted  negatively,  as  shown  by  the  dotted  line,  the  initial 
similarity  of  the  two  sequence  curves  is  evident. 

If  the  magnet  M,  figure  45,  is  reversed  into  the  position  NS  from  SN,  its 
effect  on  5  is  similar  but  only  about  half  as  large.  At  the  opposed  telephone 
T  the  use  of  a  second  magnet  gave  only  small  differences.  The  effect  observed 
is  therefore  incidental,  depending  on  the  mounting  of  the  plate  of  the  telephone. 

17.  Remarks — When  a  single  telephone  is  active,  the  opposed  plate 
functioning  like  a  rigid  wall,  the  nodal  intensity  5  was  found  to  be  about 
two-thirds  of  the  intensity  observed  when  both  are  vibrating  in  phase.  Hence, 
in  so  far  as  the  fringe  displacement  s  measures  the  nodal  intensity,  the  vibrat- 


18 


ACOUSTIC  EXPERIMENTS  WITH  THE  PIN-HOLE 


ing  plate  in  phase  action  contributes  about  as  much  intensity  as  the  fixed 
plate  reflecting. 

In  case  of  the  adjustments,  figures  3  and  5,  we  may  to  a  first  degree  of 
approximation  consider  the  vibration  vector  of  the  unloaded  telephone  T 
constant.  In  this  case  the  vibration  vector  of  the  loaded  telephone  T'  differs 
from  it  in  magnitude  and  is  set  at  a  phase  angle  with  regard  to  it,  both  of 
which  vary  with  R  and  L  in  the  above  experiments.  The  magnitude  event¬ 
ually  vanishes. 

If  we  consult  the  usual  diagram  of  relations  between  the  quantities  R,  L, 
0  =  tan_ILa;/R,  figure  46,  it  appears  that  9,  in  comparison  with  the  correspond¬ 
ing  change  of  the  current  7,  increases  most  rapidly  with  L  at  constant  R,  when 
L  is  small;  similarly  9'  =  90°- 9  in  relation  to  7  increases  most  rapidly  with  R 
at  constant  L  when  R  is  small;  for  7  under  these  circumstances  is  nearly 
normal  (diametral)  to  the  arcs  of  the  corresponding  circular  loci  of  variation. 
We  may  therefore  expect  to  find  characteristic  variations  in  the  relations  of 
9  and  7  at  the  beginning  of  the  5-curves  in  the  above  graphs,  as  observed. 

If  in  figure  47,  T  denotes  the  vibration  vector  of  the  unloaded  telephone 
and  T'  the  corresponding  vibration  vector  of  the  loaded  telephone  at  any 
instant,  T'  will  be  set  at  an  angle  to  T.  In  the  above  work  9  has  appeared  to 
be  a  lead,  while  T*  was  apparently  larger  than  T.  Hence  the  fringe  displace¬ 
ment  will  depend  on  the  difference  of  T  and  the  projection  of  T'  on  T  in  the 
sequence  curves  and  on  their  sum  (fig.  48)  in  the  phase  curves.  The  5-effect 
will  not  be  simply  additive,  however,  for  the  reasons  given  at  the  beginning 
of  this  paragraph.  Moreover,  the  5-curves  do  not  distinguish  between  sign 
changes  of  phase,  unless  the  curve  branch  is  reversed  as  in  figures  31,  37. 

Hence,  if  T'  >  T,  we  may  have  the  5-curves  passing  through  zero  (mini¬ 
mum)  in  the  sequence  graphs  by  the  simple  shrinkage  of  Tr  with  Lor  R,  where 
T  remains  constant. 

Or,  if  T'  and  T  are  appreciably  equal,  we  may  have  the  sequence  curves 
passing  with  increasing  R  through  a  minimum  usually  greater  than  zero,  by 
the  shrinkage  of  the  angle  9  taken  as  a  lead,  if  cos  9  increases  relatively  more 
rapidly  than  T'  decreases. 

Or  finally,  if  the  lead  9  passes  through  zero  into  a  lag  with  increasing  L, 
while  T'  remains  relatively  stationary  in  value,  the  5  minimum  should  be 
much  more  strikingly  reached,  and  for  T'  >  T  easily  pass  through  zero,  as 
has  been  observed  throughout  the  above  experiments.  Illustrative  cases  are 
seen  in  figures  31,  33,  37,  etc.,  recalling  that  both  an  excess  and  a  deficiency 
in  T'  may  produce  the  condition  for  a  central  node,  the  activity  passing  from 
one  telephone  to  the  other.  If  the  T'  vector  shrinks  through  zero  and  becomes 
positive  (for  reasons  of  the  kind  exhibited  in  figure  45),  figure  47  would  pass 
to  figure  48  and  the  5-curves  would  cross  for  large  R  or  L. 

The  complete  explanation  along  these  lines  would  of  course  require  a 
further  specification  of  data  than  is  now  available. 

18.  Zero  methods.  Primary  and  secondary — -The  difficulty  with  the 
above  comparisons  (equation  (4),  §  8)  lies  in  the  complicated  equations  which 


PROBE  AND  THE  INTERFEROMETER  U-GAGE 


19 


would  have  to  be  used  in  any  case  to  detach  the  L  from  the  other  quantities.* 
Greater  convenience  is  to  be  expected  if  differential  methods  corresponding 
to  the  two  circuits  of  two  telephones  T,  T'  in  operation  are  substituted.  Thus, 
for  instance,  the  adjustment  (insert,  fig.  49),  when  tested  out  by  a  millihenry 
standard  at  LT'  and  the  coil  L\  successively  in  L'T'  (secondary),  gave  results 
in  the  sequence  graph 

L  =  iomh.  5  =  24  Li  coil  only  L  =  io  mh.  s  =  10  Z,4  cored 
35  14  coil  only  14  LK  %  cored 

20  Li  M  cored 

In  figure  49  the  graphs  have  been  plotted  linearly  and  from  this  (deducting 
the  coil  effect)  35,  25,  10  mh.  would  be  estimated  for  the  wholly  or  partially 
cored  coil.  The  total  1,4  =  45  mh-  is  nearly  correct.  But  the  conditions  are 
clearly  not  so  simple.  The  phase-graph  changes  but  little  in  these  cases  (10 
mh.,  5  =  83 ;  35  mh.,  5  =  80). 

Putting  the  millihenry  standard  in  the  primary  LT,  the  results  are  even 
more  striking.  Here  10  mh.  passed  the  primary  lead  of  24  5  into  a  lag  of  10  5 
and  35  mh.  increased  this  lag  to  57  5. 

19.  Primaries  only — Tests  were  begun  with  the  adjustment  without 
secondary  adjustment  I'  shown  in  figure  50,  the  coils  inserted  at  L  and  L' 
being  compared.  The  sequence-graph  only  was  observed,  as  the  phase-graph 
varies  but  slightly.  The  upper  three  curves  show  the  results  obtained  when 
the  millihenry  was  put  in  LT  and  the  coils  only  (not  cored)  in  L'T'.  The 
resistance  of  Li  exceeds  that  of  La. 

The  two  lower  curves  give  the  corresponding  results  with  one  layer  of 
the  Li  and  the  La  coils,  cored.  In  both  cases  the  phase  difference  passes 
through  zero  (dotted  lines),  particularly  in  the  case  La.  Thus  we  obtain  the 
following  5-differences  cored-uncored : 


At  35  mh. 

Li  (cored),  As  =  37 

L\  (cored),  As  —  — 

30 

36 

21 

20 

36 

19 

10 

27 

15 

allowing  for  the  positive  and  negative  values  in  the  lower  graphs.  These 
A5  values  are  equivalent  in  the  millihenry  region  to  which  they  apply  on  the 
same  horizontal,  in  the  mean  to  La  =  3 5  mh.  and  }4Li  =  20  mh.  In  so  far  as  the 
interpretation  is  admissible,  A5  falls  off  at  the  lower  stages  (10  mh.)  in  the  table. 

In  figure  5 1  the  results  of  experiments  with  the  millihenry  standardal  one 
inserted  in  the  T'  circuit  and  also  with  the  same  standard  and  one  layer  of 
the  L2  cored  coil,  inserted  in  the  same  circuit.  The  graphs  here  would  be 
practically  straight  if  the  L\  semi-coil  could  be  taken  at  20  mh.,  which,  how¬ 
ever,  is  too  small,  unless  the  solid  core  is  ineffective. 

In  figure  52  the  measurements  for  the  La  coil  and  the  one  and  two  layered 
Li  coil  are  carried  out  with  greater  fullness.  Within  the  errors  of  reading 

*The  values  of  R  and  L  of  all  parts  of  the  apparatus  will  be  found  in  table  1  (above), 
with  which  the  present  estimates  may  be  compared. 


20 


ACOUSTIC  EXPERIMENTS  WITH  THE  PIN-HOLE 


the  results  agree  with  the  preceding  set  (fig.  50),  though  the  Li  curves  (fig. 
53)  are  straighter.  The  graphs  of  the  coil  Li,  in  whole  or  halves,  preserve  their 
characteristic  curvature.  Three  different  cores  (a,  solid;  b,  wire;  c,  two  bundles 
of  wire)  are  used.  In  the  cored  half-coil  there  is  very  little  difference  for  an 
addition  o  or  10  mh. 

As  a  rule,  the  As  values  (cored-uncored)  increase  with  L;  viz, 

£1/2  L\  Li 


0  mh. 

As  =  12 

As  =  38 

As  =27 

10 

1 7 

31 

29 

20 

24 

28 

39 

30 

22 

32 

39 

The  mean  values  are  of  the  same  order  as  before. 


If  the  initial  conditions  ( R ,  L)  in  the  two  branches  T  and  T'  are  restored, 
we  might  assume  that  the  horizontal  distance  apart  of  the  graphs  will  be  the 
L  required.  Using  this  as  an  approximation  we  get 

Li  £  =  36-0  =  36  mh.  at  5  =  11 
(Solid  core)  £1/2  £  =  26-0  =  26  5  =  12 

(Solid  core)  Lx  £  =  50-0  =  50  s  =  —  2  (prolonged) 

an  order  of  values,  like  the  preceding,  evidencing  the  ineffectiveness  of  the 
solid  core  in  L\.  The  mean  slope  of  the  curves  naturally  decreases  rapidly 
as  the  inductance  contained  increases.  Thus  in  case  of  Li,  figure  53,  5  =  1.2 
per  millihenry  falls  to  5  =  0.9  per  millihenry  after  the  Li  iron  core  is  inserted. 

The  contrast  of  the  solid  and  wire  cores  of  Li  (curves  a,  b,  c)  is  noteworthy. 
The  solid  core  was  2  cm.  in  diameter;  the  wire  core  (case  b )  consisted  of  about 

60  threads  of  iron  wire,  each  0.05  cm.  in  diameter;  the  wire  cores  (case  c) 


PROBE  AND  THE  INTERFEROMETER  U-GAGE 


21 


of  120  threads  of  the  same  wire.  If  we  imagine  the  curves  a,  b ,  c  prolonged 
till  they  intersect  the  axis  for  5  =  0,  it  will  be  seen  that  the  L  equivalent  has 
been  increased  enormously,  as  must  obviously  be  the  case  compatibly  with  the 
lamination. 

The  tendency  to  linear  graphs  for  small  inductances  and  small  increments 
of  L  is  again  apparent  in  figure  54,  where  the  weak  coil  Lw,  wire-cored  as 
stated  or  not,  is  compared  with  the  millihenry  standard.  Shifting  horizontally, 
Lw  comes  out  somewhat  less  than  10  mh. 

20.  Zero  method  with  the  secondary — With  the  adjustment,  figure  3 
(or  insert  fig.  55),  the  method  is  necessarily  less  sensitive,  because  of  the 
excess  inductance  I,  V  already  in  the  opposed  circuits.  The  graphs  obtained 
on  comparison  of  the  L4  and  Li  coils,  cored  or  not,  as  stated,  rise  with  the 
millihenries  opposed  but  slowly.  They  are  farther  apart  in  case  of  L\  (fig.  56) 
than  of  Li  (fig.  55),  because  of  the  solid  core  and  the  inherently  greater  resist¬ 
ance  in  the  latter  case.  This  method  therefore  contemplates  the  comparison 
of  large  inductances  and  would  in  such  a  case  show  acceptable  results,  as 
already  indicated  in  the  preceding  work. 

21.  Exchange  of  loads.  Circuits  in  parallel — The  above  relations  are 
throughout  complicated.  It  was  therefore  thought  desirable  to  devise  means 
for  exchanging  inductances  only.  The  adjustments  are  indicated  in  the 
insert  of  figure  57,  where  T  and  T'  are  the  opposed  telephones,  E  the  cell  with 
periodic  break,  B  and  5,  S'  switches  for  reversing  the  current  in  T  or  Tr.  The 
inductances  L  and  L'  can  be  inserted  either  into  the  circuits  T  and  T'  respec¬ 
tively,  as  in  the  figure,  or  reversed  so  that  L  is  inserted  into  the  T'  and  L' 
into  the  T  circuit.  This  is  done  by  the  four-fold  commutator  K,  in  which  the 
brass  strips  a,  when  pointing  toward  the  left,  join  the  corresponding  four  con¬ 
tacts  (1  to  4)  below,  or  when  pointing  to  the  right  (swivel)  join  the  contacts 
3  to  6  below.  Contacts  1  and  5,  2  and  6  are  metallically  joined,  and  1  and  2 
or  5  and  6  contain  the  inductance  L,  3  and  4  the  inductance  L' .  *  The  position 
of  the  strips  a,  as  in  figure,  will  be  denoted  by  7,  the  other  portion  by  77; 
so  that  for  7,  L  is  in  the  T  and  L'  in  the  T'  circuit. 

In  the  experiments  following  L  is  the  continuously  variable  millihenry 
standard,  L'  the  coil  L\  with  or  without  iron  cores,  solid  or  fasciculated  wire 
as  stated  (see  scheme  in  figure  57).  The  fringe  displacements  5  obtained  are 
given  in  figure  57  for  loads  L  of  10,  20,  30  millihenries  as  abscissas,  when  the 
counter-load  is  the  coil  Li  only.  In  figure  58  the  solid  iron  core  is  thrust  into 
Li  and  in  figure  59  the  core  is  of  wire.  The  three  cases  represent  a  succession 
of  increasing  inductance  with  the  resistances  constant. 

The  phase-graphs  usually  present  no  marked  peculiarity.  Their  mean 
5-values  (7  and  II)  decrease  with  the  load  Li,  while  at  the  same  time  the 
graphs  nearly  coincident  in  figure  57  (un cored)  separate  widely  in  figure  59. 
The  II  graph  in  59  is  in  part  even  above  the  II  graph  in  figure  58  for  a  lower 
value  of  L\. 


22 


ACOUSTIC  EXPERIMENTS  WITH  THE  PIN-HOLE 


Very  characteristic  differences  appear  in  the  sequence-graphs.  In  figure 
57  the  observed  graphs  cross.  This  indicates  deficient  singing  in  the  position 
I  of  the  millihenry  circuit,  since  the  graph  rises  with  the  increasing  millihenry 
inductance,  while  the  Li  (coil)  circuit  carries  the  sound.  The  graph  II  has 
therefore  been  reversed  into  the  dotted  line  II',  figure  57,  for  now  the  opposite 
conditions  rule.  The  two  graphs  are  parallel  and  the  rate  is  about  1.1  5/milli¬ 
henry  for  each. 

In  figure  58  the  sound  is  carried  by  the  millihenry  standard  circuit  in 
both  positions  I  and  II.  The  impedance  Li  is  now  excessive.  The  graphs 
have  therefore  been  reversed,  as  shown  in  I'  and  II' .  The  two  graphs  are  here 


farthest  apart.  The  mean  rates  are  respectively  0.8  5/millihenry  for  case  I' 
and  0.6  5 /millihenry  for  case  II'. 

In  figure  59  the  relations  are  of  the  same  nature,  but  reach  a  higher  degree 
of  displacement.  The  reversed  curves  I'  and  II'  are  lower  than  before,  but 
(unexpectedly)  nearer  together.  The  rates  have  decreased  further  to  0.7 
5/millihenry  for  case  I  and  0.4  5/millihenry  for  case  II.  This  gradual  fall  of 
rate  is  summarized  in  the  insert  a  in  figure  59. 

The  drop  below  the  corresponding  graphs  of  figure  5  7  has  been : 


Fig 


(2){ 


58 

I 

II 

Fig.  59  I 

II 

10  mh. 

*  =  34 

34 

10  5  =  64 

47 

20 

34 

40 

20  66 

54 

30 

37 

43 

30  67 

61 

Mean 

*  =  35 

39 

5  =  66 

54 

/Mean  rates  5/mh.  .80 

.60 

.70 

.40 

1 L  estimated 

44 

65  (solid  core) 

94 

135 

/Mean  rates  5/mh.  .90 

.83 

\L  estimated 

39 

47  (solid  core) 

135  mh.  (wire  core) 


Since  in  each  of  the  positions  /  and  II  there  is  a  mere  exchange  of  the 
excess  inductance,  the  first  results  (1)  are  rather  disappointing.  The  reason 
of  this,  however,  is  the  rapid  change  of  the  rates  of  fringe  displacement  per 


PROBE  AND  THE  INTERFEROMETER  U-GAGE 


23 


millihenry  s/mh.  as  the  load  L  increases.  Thus  it  is  better  to  take  the  mean 
rate  of  the  initial  graphs  (fig.  57  s/mh.  =  1  for  position  I  and  1.05  for  II) 
and  the  final  graph  in  question.  In  this  way  it  was  thought  the  results  (2) 
would  be  improved  as  a  whole  and  rendered  more  trustworthy.  In  figure  58 
the  trouble  is  to  be  associated  with  the  curved  graphs.  The  effect  of  lamina¬ 
tion  has  thus  increased  the  inductance  more  than  twice,  but  the  estimates  are 
all  too  low. 


Finally,  a  comparison  of  the  As- values  (phase  minus  sequence)  may  be  given : 


Induct¬ 

ance 

10 

20 

30 

10 

20 

30 

10 

20 

30  mh. 

Posi¬ 
tion.  . 

7  II 

7  II 

7  77 

7  77 

7  77 

7  77 

7  77 

7  77 

7  77 

As .... 

—  106  —  148 

-95  -133 

-84  -132 

123  172 

113  167 

104155 

144  187 

135  179 

125  172 

As—As0  . 

17  24 

18  34 

20  33 

38  39 

40  46 

4i  50 

The  data  for  As  — As0,  which  indicate  the  difference  between  the  cases  of 
cored  and  uncored  coils,  are  here  far  from  constant,  particularly  in  the  position 
II.  They  are  also  not  much  more  than  half  as  large  as  the  corresponding 
s-values  of  the  preceding  table. 

Apart  from  irregularities,  the  data  for  As  make  a  coherent  graph  of  rising 
inductances  as  shown  in  figures  60,  61,  62.  For  the  position  I  the  rates  are 
nearly  the  same;  for  the  position  II,  for  some  reason,  there  is  irregularity, 
the  mean  results  being: 


Position 

Coil 

Solid  core 

Wire  core 

^  ^  [I . 

I. IO 

0-95 

•9 

18 

0.95  $/mh. 

•75 

40 

45 

Rates  \  TT 

l  ••••••••••• 

1-3 

A  .  I . 

Mean  A.s-Aj0<  jj 

30 

\  «*••••  • 

The  smoothed  data  for  L  so  to  be  found  would  be  far  too  small.  They  are 
only  about  half  as  large  as  obtained  from  the  sequence-graph  alone.  Since 
the  phase  and  sequence  graphs  trend  toward  each  other,  such  a  discrepancy 
would  be  expected;  but  it  was  not  estimated  to  be  so  large. 

22.  Further  experiments — It  appears  from  the  preceding  methods  that 
the  sequence-graph  taken  alone  is  better  adapted  for  practical  purposes  than 
the  combined  graphs  (As).  A  number  of  further  experiments  were,  therefore, 
tried  out  with  the  coils  of  small  resistance  L4  and  Lw.  The  data  were  given  for 
the  latter  in  figures  63,  64,  65  with  the  coil,  Lw ,  respectively  empty,  cored  with 
solid  iron,  and  wire  cored.  From  these  one  obtains : 


Coil  empty 

Solid 

core  in 

Wire  core  in 

Position .  7 

77 

7 

77 

7 

77 

Mean  s=  36 

0 

32 

—2 

27 

-5 

Mean  s—s0  .... 

•  • 

4 

2 

9 

5 

Rate  r  1.05 

•5 

1. 10 

•55 

1.0 

•75 s/  mh. 

Mean  (r  +  r0)/ 2  . . . 

•  • 

1.07 

•52 

1.03 

.63 s/  mh. 

Estimated  Lw  ... 

•  • 

3-7 

3-9 

8.8 

8.0  mh. 

3 


24 


ACOUSTIC  EXPERIMENTS  WITH  THE  PIN-HOLE 


so  that  for  positions  I  and  II  the  agreement  is  within  i  millihenry  and  not 
much  below  the  true  values  1 1  mh. 

For  the  coil  L4  similarly  (figs.  66,  67) : 


Coil  empty 

Coil  wire  cored 

Position . 

I 

II 

I 

II 

Mean  s . 

33 

—  1 

+  I 

-33 

Mean  s— s0 . 

•  •  •  • 

•  • 

32 

32 

Rate  r . 

1.05 

•4 

•4 

1.05 

Mean  rate  (r  -f  r0)  / 2 . 

•  •  •  • 

•  • 

.72 

•73 

Li  estimated . 

•  •  •  • 

•  • 

44 

44  mh. 

data  which  happen  to  coincide.  Results  computed  from  the  individual 
observation  at  10,  20,  30  millihenries  of  the  standard  give  practically  the 


same  values  and  are  nearly  correct.  Readings  near  zero  are  usually  trying, 
because  the  small  displacements  and  slow  accommodation  of  fringes  make  it 
difficult  to  pick  out  the  resonance  pitch.  As  the  rate  for  mean  5  =  0  is  large, 
this  difficulty  makes  such  measurements  rather  crude.  A  sharp  adjustment 
in  pitch  is  essential,  and  at  5  =  0  a  tendency  to  multiresonance  is  often  in 
evidence. 

A  number  of  similar  experiments  were  completed,  without,  however,  reach¬ 
ing  any  marked  improvement,  and  a  uniform  schedule  of  rates  (s/mh.)  at 
definite  mean  5-values  could  not  be  constructed.  For  example,  on  com¬ 
paring  a  given  coil  of  two  parallel  layers  with  a  single  one  of  its  layers,  results 
(figs.  68,  69)  were  obtained  in  which  the  means  only  were  in  proper  ratio. 
Thus  2L  =  83  I;  107,  II;  mean  95  mh.,andL  =  34  I;  66,  II;  mean  50  mh. 
etc.,  point  out  an  inductive  difference,  or  else  a  difference  in  sensitiveness  in 


PROBE  AND  THE  INTERFEROMETER  U-GAGE 


25 


the  telephones.  Figure  69,  moreover,  indicates  a  serious  case  of  the  difficulty 
of  obtaining  the  rates  s/ mh.  when  mean  s  =  o.  It  was  necessary  to  inter¬ 
polate  them.  In  the  half-coil,  the  discrepancy  of  the  halved  resistance  must 
first  be  allowed  for. 

In  the  further  measurements  of  the  relative  inductance  of  coil,  and  half¬ 
coil  with  large  fringe  displacements  (3  storage-cells  in  circuit) ,  the  proportion¬ 
ality  of  the  displacement  5  to  the  effective  currents  seems  to  have  broken 
down.  Thus 


*1  TT 


L  = 

=  10 

20 

30  mh. 

Mean  rate 

A  s  = 

=  62 

60 

62 

1.6 

68 

68 

68 

.8 

A  5  = 

=  96 

100 

108 

•95 

66 

6  7 

86 

•75 

84/ 


The  individual  results  are  given  in  the  usual  way  in  figure  70,  the  circuits 
being  adjusted  as  in  figure  57.  The  plan  of  assuming  proportionality  between 
the  displacements  As  and  rates  (s/mh.)  together  with  the  effective  currents, 
is  of  course  a  shortcoming  of  the  method  pursued,  as  a  whole,  and  was  merely 
adopted  tentatively.  With  an  increase  of  range,  the  discrepancy  becomes 
rapidly  more  noticeable. 


To  throw  additional  light  on  these  phenomena  (cf.  §  14)  resistances  R  in 
two  identical  rheostats  were  directly  compared  as  detailed  in  figure  7 1 .  Keep¬ 
ing  the  resistance  of  one  circuit  constant  (R  —  o,  100,  500  ohms)  the  other  was 
increased  in  steps.  The  graphs  show  at  once  that  one  telephone  is  more 
efficient  than  the  other.  There  seems  to  be  no  crossing  of  curves  here,  indicat¬ 
ing  that  the  change  of  phase  due  to  R  is  not  of  much  importance,  R  being 
usually  large.  The  response,  moreover,  is  feeble  for  excess  resistances  above 
a  few  hundred  ohms  in  one  of  the  circuits,  unless  more  cells  are  put  in  use. 
This  implies  correlative  limitations  in  the  Lw  work,  although  the  phase-change 
is  here  continuous. 

It  is  also  probable  that  this  difference  of  response  will  vary  with  temper¬ 
atures,  owing  to  expansions  of  the  case  holding  the  telephone-plate. 


26 


ACOUSTIC  EXPERIMENTS  WITH  THE  PIN-HOLE 


If  we  consider  the  distribution  of  current  in  the  parallel  circuits  T  and  T' 
and  write  Ri  =  e  —  const.,  etc.,  the  equations  reduce  to 

io  (i  —Ro/R)=Ai 

where  Ro  is  the  resistance  kept  constant  in  one  of  the  circuits.  Hence  if  the 
sequence  condition  is  perfect,  Ai  =  o,  and  R  =  Ro,  where  R ,  Ro  include  the 
initial  resistances  as  well  as  the  added  resistance.  This  presupposes  that  the 
telephones,  etc.,  are  identical  and  makes  no  allowance  for  their  inductance. 
If  the  plate-mounting  of  one  contributes  to  greater  sensitiveness  than  the 
other,  Ai  —  o  is  a  spurious  balance,  as  in  the  case  of  figure  71.  The  subject 
will  be  treated  in  the  next  section. 


23.  Summary.  Quantitative  considerations — The  results  contained  in 
the  graphs  submitted  imply  that  the  two  telephones  are  unequally  sensitive. 
This  is  a  little  puzzling,  since  their  resistances  and  inductances  are  the  same 
(R  =  84  ohms,  L  =  0.06  hen.)  and  the  resistances  of  the  standard  (R  =  9.7  ohms) 
and  of  the  standard  coil  (^  =  9.9  ohms)  are  about  the  same.  Everything 
should  therefore  depend  on  the  external  resistance  or  inductances,  and  if 
these  are  the  same  there  should  be  no  change  of  fringe  displacement,  s,  on 
commutation. 

The  difference  in  the  paired  and  similar  telephones  may  be  due  to  the  set 
of  the  plates;  but  as  it  occurs  very  uniformly,  so  far  as  I  have  observed,  it 
probably  results  from  an  induction  impulse  chiefly  in  one  direction.  In  case 
of  the  sequence-graph,  the  plates  of  the  telephone  would  therefore  be  attracted 
and  released,  respectively,  at  any  given  time.  These  forces  are  liable  to  be 
unequally  strong,  the  attraction  probably  being  in  excess. 

Hence  if  we  call  the  amplitudes  or  displacement  vectors  of  the  plate  T' 
and  T,  where  T '  >  T,  the  postulates  T'  cos  0  <  T  slightly,  and  T'>T  cos  0  in 
marked  degree  would  account  for  most  of  the  observations,  if  0  is  the  lag  due 
to  the  inductance  L,  initially.  Subsequently  T  or  else  T'  are  reduced  by  the 
successively  increasing  inductance  L  of  the  standard,  as  indicated  by  the 
diagram  (fig.  72).  In  case  I  the  graph  rises;  in  case  II  the  observed  graph 
falls  and  5  =  o  is  reached  much  later. 

Since  tan  0  =  Lu/R  and  L  —  0.38  hen.  (cored  coil  0.32,  telephone  0.06)  while 
R  =  94  ohms  (coil  10,  telephone  84)  and  60  =  2,765,  we  find  tan  0=11.2,  or 

0  =  84.9°,  and  V^2 -f  L2co2  =  1,054  ohms,  Leo  =1,050. 

On  the  side  of  the  standard  ^  =  94  ohms  also,  while  the  L  changes  from 
0.010  to  0.035  hen.,  thus 


L  =  0.010 
_ Q  =  1 6.4° 

VR2  +  LW  =  98 
Lo)  =  27.6 


0.020  0.030  hen. 

30.50  41. 40 

hi  125  ohms 

55.3  82.9  ohms 


when  L  and  the  standard  are  exchanged,  the  specifications  (except  L)  remain 
about  the  same. 


PROBE  AND  THE  INTERFEROMETER  U-GAGE 


27 


If  we  take  the  case  of  the  sequence-graph,  since  the  currents  i  and  i'  in 
the  branches  T ,  T'  (fig.  57,  inset)  are  in  parallel, 

s  =  *  Vf?  +  L V = i'  V R'2  +  L'W  =  M/A  Vi?2  +  L V 

follows  as  usual.  But  as  the  equality  of  fringe  displacements  s,  s',  is  primarily 
in  question,  we  may  then  postulate  for  small  currents,  i—s/c  and  i'  =s'/c', 
in  view  of  the  difference  of  telephones  in  question.  Hence  the  last  equation 
reduces  to 

£  =  A s/(c/  Vi?2  +  iy-  c'/  V i?'2  +  L'v) 


If  As  =  o  in  the  sequence  graph,  the  denominator  must  also  be  zero.  Thus 

R2  +  LV  =  (c/c'  )2  (. R '2  +  L'V). 

Here  the  values  of  R,  L,  etc.,  are  the  total  resistances  and  inductances.  If 
we  replace  R  by  R  +  R0,  L  by  L  +  L0,  etc.,  where  R,  L  are  the  external  and 
Ro,  Lo  the  internal  data,  the  modified  equation  is 

(R+R0)2  +  (L  +  Lo)V  =  (c/c')2  ( (R'  +  R'o)2  +  (L'  +  Lo)  V) 

This  equation  on  commutation  becomes 

(Ri  +  Ro)2  +  (Lx  +  Lo)  V  =  (c/c')2  ( (R'l  +  R'o)2  +  (L'l  +  L'o) V) 

where  L\  and  L'  are  read  off  on  the  standard. 


Now,  in  the  above  circuit  the  resistances  R  are  the  same ;  i.  e.,  R  =  R'  =  Ri  = 
R'i\ ;  Ro  =  R'o,  also  Lo  =  L'0,  and  L—L\  is  the  constant  exchanged  inductance. 
Hence  if  we  subtract  the  two  equations 

(L  +  Lo)2  -  (L,  +  Lo)2  =  (c/c')2  { (1/  +  Lo)2  ■ -  (L  +  Lo)2 } 

This  equation  determines  L  if  c/c'  is  known  for  a  previous  determination  with 
known  L  and  Lo,  since 

/c_  y=  (L  +  Lp)2 — (Lx  +  Lo)2 
Vc'/  (Lr  +  Lo)2 — (L  +  L0)2 
where  Li  and  L'  are  given. 

The  difficulty  of  applying  this  equation  to  graphs  figure  57  et  seq.  is  that 
As  —  o,  or  the  intersection  of  the  graphs  with  the  abscissa  would  have  to  be 
extrapolated,  and  this  is  only  feasible  in  figure  57,  where  unfortunately  the 
Lo  of  this  coil  without  core  was  not  directly  determined;  but  equation  states, 
nevertheless,  if  the  data  given  be  inserted, 


(L+6o)2— (65)2 
(100)2—  (L  +  60)2 


so  that  L  must  lie  between  40  and  5  mh.;  or,  since  c/c'>  1,  between  25  and  5 
mh.  In  general,  however,  i  —  s/c  is  not  adequate,  the  more  approximate 
equation  being  of  the  form  so  =  seto/t,  which  is  here  inconvenient. 

When  the  sequence-graphs  cross,  as  in  figure  57,  the  unknown  inductance 
is  determinable  at  once.  If  we  rewrite  the  first  of  the  above  equations  and 


28 


ACOUSTIC  EXPERIMENTS  WITH  THE  PIN-HOLE 


remember  that  here  R  =  R',  etc.,  that  L  (constant)  is  exchanged,  As/  e  remain¬ 
ing  constant  on  commutation, 

VW+  iv  .  V.R2  +  iv 
C  +  C  C  Vr2  +  L'lV  +  °  Vi?2  +  L' V 

but  at  the  point  of  intersection  L\  =  L'i  whence  L  =  L\.  In  figure  5 7 ,  therefore, 
the  inductance  of  the  coil  is  23  mh. 

From  this  and  the  numerical  equation  for  ( c/c ')2  the  result  is 

,  ,  V4421 

c/c  —  *  I*I9 

V3111 

indicating  the  degree  of  inequality  of  the  two  telephones  in  relation  to  the 
sequence  graphs  and  resulting  from  the  asymmetry  of  vibration  of  plates. 

Such  cases  as  figures  58,  59,  etc.,  would  have  needed  a  much  larger  stand¬ 
ard  of  comparison,  L. 

Graph  71,  obtained  with  the  mere  exchange  of  resistances,  merits  some 
further  attention.  If  R  is  the  fixed  resistance  commutated,  R'  and  R"  the 
counter-values  corresponding  to  positions  I  and  II,  since  internally  L'0  =  L'o 
and  R0  =  R'o,  the  equations  reduce  to 

_ c  +  c' _  = _ £ _ I _ c_[ _ 

V{R  +  i?0)2  +  i«v  Vo?"  +  i?o)2  +  loV  V(i?'  +  i?o)2  +  W 

A  solution  of  this  equation  is  R'  —  R" —R,  so  that  the  paired  curves  of  figure 
71  intersect  near  R  =  o,  R  =  100,  R  =  500  ohms. 

The  case  of  As'  =  o  and  A5"  =  o,  for  the  two  positions  I  and  II,  is  available 
for  R=ioo  ohms.  The  other  cases  (R  =  o  and  R  =  500)  do  not  reach  the 
abscissa.  We  thus  have  again 

,  V(i?  +  i?0)2  +  L«V  V(i?"+i?0)2  +  LV 
c  V(i?'  +  i?o)2  +  LoV  V(R  +  R„y  +  LW 

If  we  insert  the  values  R  — 100,  R'  =  50,  R"  —  1 50  ohms,  as  given  by  the  graphs 
and  the  constants  Lo  =  o.o6  and  ^  =  84,  we  obtain  c/c'  =  1.16,  in  both  cases, 
which  agrees  very  well  with  c/c'  =  1.19  deduced  from  inductances,  in  the  pre¬ 
ceding  section. 

In  the  semi-coil  graphs  in  figure  69,  another  case  of  intersection  occurs  at 
about  L  =  0.007  henry.  The  equations  for  As'  — As"  (positions  I  and  II  with 
identical  As),  R/ 2  and  L/ 2  for  the  coil  would  now  be: 

_ c  +  c’ _ 

V(R/ 2  +  RoY  +  ( Lo  +  L!  2)  V 


V(R  +  R0y  +  (Lo  +  LOV  V(i?  +  i?0)2+(Lo  +  L")V 


PROBE  AND  THE  INTERFEROMETER  U-GAGE 


29 


Since  L!  —  L"  at  the  intersection,  the  equation  reduces  to 

R2 


(Io + h )  - 


■ORo  +  3L/4)  +  (Lo  +  L’)2 


cox 


Inserting  Lo  =  o.o6,  R=  io,  03  =  2,765,  L'  =  0.07,  the  value  of  L  =  0.016  henry 
is  obtained. 

We  can  here  also  use  the  datum  Li  for  As  =  o  by  prolonging  the  graph  I 
till  it  meets  the  abscissa.  Thus  Li  =  io  mh.  and  the  corresponding  L2  =  3 o  is 
found  directly  from  the  graph  II.  Here  the  equation  reads 

(R/ 2  +  R0)2  +  (Lo  +  L/2)2  032  {R  +  Ro)2  +  (Lo  +  L2)  V 


(7)'- 


(R  +  Ro)2  +  (Lo  +  UY  032  (R/2  +  RoY  +  (Lo  +  L/2)  V 


Equating  these  values,  reducing  and  inserting  the  data  given,  the  result  is 
L  =  0.019  henry.  The  inductances  16  and  19  mh.  are  both  low  as  compared 
with  L  =  23  mh.  inferred  from  the  double-coil  measurement;  but  the  trouble 
lies  in  the  crude  graph  used  and  not  in  the  method  and  could  be  easily  rectified. 

24.  High-resistance  telephones.  Zero  methods — It  was  anticipated 
that  in  dealing  with  larger  inductances,  the  radio  telephones  would  be  more 
useful.  Furthermore,  an  enlargement  of  the  end  connections  of  the  pipe 
joining  the  paired  telephones  suggested  itself.  The  junction  above  was  made 
with  the  aid  of  perforated  rubber  stoppers  and  quill-tube  connectors.  In  the 
present  case  the  tube  ends  were  attached  to  the  telephone  mouthpieces  with 
cement,  directly,  in  order  to  introduce  the  least  obstruction  possible.  The 
result,  however,  was  but  a  slight  rise  in  pitch,  from  the  a'  above  to  W  in  the 
present  adjustment. 

At  the  outset  great  confusion  was  experienced,  afterwards  traced  to  a 
slightly  loose  cap  in  one  telephone.  With  the  parallel  adjustment  of  figure 
73,  the  telephones  together,  and  for  positions  I  and  II  of  the  switch,  gave  at 
the  maximum  but 

I:  5  =  65,  c"  II:  s  =  so,d" 

with  a  decided  difference  in  pitch.  The  telephone  T  alone  gave  I:  s  —  o  and 
II:  5  =  50,  a'  to  s  =  20,  e",  data  which  indicate  the  seriousness  of  even  a 
slight  leak. 

After  remedying  the  defect,  the  individual  telephones  showed 


T 


V 


I:  s— 100, 
II:  s—  60,  b6 


I:  5  =  120,  b b 
II:  70,  b b 

The  pitch  has  thus  become  fixed;  but  the  telephone  circuits  are  nevertheless 
unequally  responsive;  while  both  are  more  sensitive  in  the  I  position  than 
in  the  II  position  of  the  switch  (switches  being  here  provided  for  both  tele¬ 
phones).  This  is  probably  the  inevitable  exchange  of  attraction  and  release 
already  discussed. 

To  use  the  telephones  together  it  was  necessary  to  reduce  the  storage-cells, 
L,  from  3  to  2.  Even  then  the  fringes  at  W  and  b b"  pitch  went  just  out  of  the 


30 


ACOUSTIC  EXPERIMENTS  WITH  THE  PIN-HOLE 


field.  Figure  73  gives  evidence  of  the  extreme  sharpness  of  the  resonance 
crests  for  the  I  position  of  the  switch  (phase).  Below  e\  however,  there  is 
multiresonance  which  is  difficult  to  construe,  as  a  definite  bb  crest  could  not  be 
found,  unless  the  c'  crest  here  replaces  it.  The  occurrence  of  the  sharp,  strong 
W'  crest  must  have  had  an  analogue  in  the  above  work,  though  for  some 
reason  it  was  not  detected.  It  may  have  been  deadened  by  the  quill-tube 
connectors. 

The  sequence  curve,  figure  74,  is  very  weak  throughout  and  practically 
without  elevation  at  Wf  and  W.  It  has,  however,  picked  up  its  own  small 
harmonies  at  f  and  f"  with  a  little  one  at  b.  It  follows  that  the  balance  in  the 
absence  of  auxiliary  inductances  and  resistances  is  apparently  rather  better 
here  than  above,  but  this  is  probably  due  to  the  fact  that  the  currents  are 
now  excessive,  i.  e.y  the  limit  displacement  of  both  telephone-plates  has  nearly 


been  reached  in  each  telephone,  so  that  small  differences  of  current  are  no 
longer  registered.  Similarly,  the  inductions  may  reach  limits. 

It  is  interesting  to  inquire  into  the  cause  of  the  /  crests  in  the  sequence- 
graph  (fig.  75)  and  the  suggestion  is  at  hand,  since  the  /  is  the  fifth  of  and 
the  telephone  note  is  rich  in  overtones.  In  the  sequence-graph,  therefore, 
while  the  bfr  is  eliminated,  the  /  overtone  would  not  be.  In  fact,  if  we  take 
the  usual  equations  y  =  a  sin  (<p-<po)  and  y'  =  a'  sin  (< the  compound 
harmonic  is  y+y'=A  sin  (3>-^o)  where  tan  $0=2a  sin  <p0/2a  cos<p0  and  A2  = 
(2a  sin  (po)2+  (2a  cos  <p0)2.  Hence,  if  we  put  a  =  a',  <p0  =  o  and  (p'o  =  tt/2  for  the 
/ harmonic,  it  follows  that  $0  =  45°  and  A=a\/ 2 ;  so  that  the/  is  not  eliminated 
but  appears  \/ 2  times  more  strongly  in  the  compound  note  than  in  either 
harmonic  separately. 

For  the  \>b  phase-graph  in  the  same  way  A  =a+a'  and  for  the  sequence- 
graph  A  =  a-a'  =  o,  as  hitherto  assumed.  A  divergence  enters,  however,  as  5 
is  only  proportional  to  the  effective  current  within  a  small  range  near  the  origin. 


PROBE  AND  THE  INTERFEROMETER  U-GAGE 


31 


In  the  balanced  sequence-graph  there  is  probably  no  audible  fundamental 

inasmuch  as  a  single  wave  runs  from  end  to  end  of  the  tube  without 
interference. 

25.  The  same  with  small  inductor — As  it  is  the  chief  purpose  of  the 
present  adjustment  to  meet  the  case  of  large  resistances  and  inductances,  the 
small  inductor  7,  figure  75,  was  inserted  as  there  shown,  using  the  device  C 
for  the  exchange  of  auxiliary  inductances  L,  L',  etc.,  as  already  explained. 
Each  telephone,  T,  T't  has  its  own  secondary  and  Tf  is  provided  with  a  switch 
5.  B  is  the  periodic  break.  Under  these  circumstances  a  single  cell  at  e  will 
throw  the  crests  of  the  phase-graph  far  out  of  the  field  of  view,  the  curve 
in  the  absence  of  external  inductances  rising  nearly  twice  as  high  as  in  figure 
73.  The  sequence-graph  (fig.  75)  is  correspondingly  developed  with  the  / 
crests  sharper  than  in  figure  74.  The  strong  b  crest  here  obtained  is  a  new 
feature  and  there  was  a  further  marked  development  even  as  low  as  c.  These 
crests,  however,  are  to  be  avoided  and  the  measurements  made  corresponding 
to  the  sharp  W'  or  W  resonance  in  the  phase-graph.  Taken  singly,  the  tele¬ 
phones  produce  fringe  displacements  of  5  =  120  to  130,  one  of  the  telephones 
being  kept  free  from  current.  Taken  together  in  sequence,  there  is  no  dis¬ 
placement  at  \>b' ,  as  figure  75  shows. 

There  are  two  difficulties  encountered  in  making  these  experiments:  The 
first  is  the  sharpness  of  the  resonance  crests;  the  other,  the  rather  slow  growth 
of  the  maximum  displacement.  There  seems  also  to  be  a  loss  of  sensitiveness 
in  the  lapse  of  time,  for  which  many  reasons  might  be  assigned.  Hence,  in 
the  examples  given  in  figure  76  of  the  effect  of  auxiliary  resistances  (R  =  o  to 
40,000  ohms)  in  the  T  and  T'  circuits,  there  is  often  a  lack  of  precision  in  the 
graphs.  The  data  5  refer  to  a  resistance  R  (in  thousands  of  ohms)  in  the  T 
circuit  and  R'  in  the  T'  circuit.  The  limiting  fringe  displacements  for  R'  =  00 
is  also  indicated.  The  dotted  lines  are  reversals,  showing  change  of  phase 
between  telephones.  The  results  here  are  practically  the  same  on  commu¬ 
tation.  In  case  of  R' =  o,  the  curve  given  is  probably  nearly  right.  When 
R' =  10,000  or  20,000,  the  sensitiveness  soon  drops  off.  In  the  latter  case 
neither  R  =10,000  nor  R  —  20,000  give  perceptible  fringe  deflections  and  for 
R  =  a?  f  5  =  25  only.  As  the  displacement  vector  of  the  T'  plate  decreases  with 
Rr}  the  excess  of  the  T  plate  vector  is  first  registered  in  the  sequence  graphs 
and  ultimately  (R—  «)  the  excess  of  the  diminished  T'  vector.  This  is 
indicated  figuratively  at  a,  figure  76. 

The  endeavor  to  compensate  a  resistance  by  an  inductance  is  marked 
by  more  complicated  behavior.  To  begin  with,  a  relatively  small  inductance 
of  the  wire-cored  coils  Li,  and  Li,  it  was  desirable  to  enlarge  the  sequence 
graphs  by  using  the  storage-cell  with  20  ohms  resistance  in  the  primary  instead 
of  the  former  30  ohms.  The  graphs  a  of  figure  77  are  for  this  reason  higher 
than  in  figure  76  and  the  phase-graph  would  be  quite  beyond  the  field  charted. 
Considering  the  difficulties  mentioned,  the  graphs  of  figure  77  are  satisfac¬ 
torily  smooth.  They  show  that  in  the  77  positions  of  the  double  commutator 


32 


ACOUSTIC  EXPERIMENTS  WITH  THE  PIN-HOLE 


( C ,  fig.  7  5)  no  balance,  but  only  a  flat  minimum,  is  possible,  whereas  in  the 
I  position  the  balance  occurs  (appreciably  at  least)  at  A!  =  o.  The  lines  a,  I 
and  II,  intersect  at  about  7?  =  4,000  ohms. 

To  further  exhibit  this  behavior  a  larger  inductance  L3  given  by  the 
secondary  of  a  small  lecture  model  of  an  induction  coil  (6  cm.  long,  4  cm. 
diam.),  from  which  the  core  could  be  withdrawn,  was  tested.  The  results  are 
given,  figure  776,  and  are  a  further  development  of  the  a  set,  inasmuch  as  the 
minima  now  appear  for  both  positions  I  and  II  of  the  C  commutator.  These 
curves  would  intersect  at  about  40,000  ohms,  probably,  as  the  fringe  dis¬ 
placements  when  R=  co  are  greater  for  position  I  than  for  II  of  the  commu¬ 
tator  C.  Initially  curve  I  is  always  below  curve  II,  as  in  curve  a. 

Finally  (fig.  78,  R'  —  0),  the  graphs  for  the  combined  inductances  Li+L3-f- 
L4  were  tried  out.  They  correspond  very  closely  to  the  b  curves  of  figure  77. 
The  s  displacements  are  naturally  throughout  smaller.  The  minima  are  a 
more  pronounced  feature  of  the  graphs  and  farther  to  the  right. 


The  endeavor  to  bring  these  graphs  ( R'  =  o )  to  approximate  coincidence 
at  the  beginning  ( R'  —  o ),  by  inserting  additional  resistance  (AR  =  3,000)  in 
one  of  the  T  circuits  gives  rise  to  the  curious  increased  departure  from  each 
other  of  the  two  graphs,  also  exhibited  in  figure  78.  The  coincidence  has,  as  it 
were,  been  displaced  from  R  =  40,000  to  R  =  o. 

Thus  the  evidence  indicated,  in  the  first  place,  that  the  paired  secondary 
coils,  I',  I ",  of  the  inductor  I  of  figure  75,  are  unequal.  To  test  this  directly, 
excess  resistances  R  and  R'  are  again  compared  as  in  figure  76,  but  with  the 
present  enhanced  sensitiveness  seen  in  figure  79.  The  curve  R'  =  o,  for  posi¬ 
tion  I,  is  here  throughout  above  the  curve  of  II,  even  though  the  latter  begins 
as  usual  with  the  suggestion  of  a  minimum. 

Available  inductances  larger  than  L3  were  not  at  hand  and  the  usual 
laboratory  induction  coils  if  inserted  must  act  much  like  a  break  circuit. 


PROBE  AND  THE  INTERFEROMETER  U-GAGE 


33 


26.  Compensating  inductances — 'The  endeavor  to  equalize  the  coils 
I ' ,  I"  of  the  same  inductor  would  have  been  extremely  laborious.  Since  the 
telephones  are  not  equally  sensitive,  figure  80  gives  an  example  of  results 
obtained  on  inserting  a  small  inductance  A L  in  the  T  or  T'  circuit,  respectively, 
and  then  removing  it  (AL  =  o).  The  curves  are  worked  out  for  both  positions 
of  the  commutator,  which  does  not  of  course  commutate  A L.  As  in  case  of  the 
ballast  in  figure  78,  it  is  so  hard  to  follow  what  is  taking  place  that  the  graphs 
are  not  suggestive.  Thus  for  resistances  below  R=  io4  ohms,  the  graphs 
AL  =  o,  II  and  A L,  T ,  II,  as  well  as  the  graphs  AL  =  o,  I,  and  A L,  V ,  I,  could 
be  made  to  nearly  coincide  by  a  slight  lateral  displacement  of  one  of  the  curves 
of  a  pair.  A L,  T',  II,  and  A L,  T,  I,  lie  apart.  If  we  tabulate  these  adjust¬ 
ments,  viz, 

I  II 


(1) 

(3) 


T  V 

Li  R  T  A L 
Lx  R 
Li +  AL  R 


T 
R 

R  L 
R  +  AL 


V 

Li  +  A L  (3) 


it  will  be  seen  that  the  cases  (1)  and  (2)  are  mere  shifts,  as  specified,  whereas 
the  parts  of  the  diagonal  case  (3)  are  effectively  distinct  curves.  This  means 
that  the  fringe  displacement  s  is  not  much  changed  when  A L  is  added  on  the 
R  side;  but  that  the  graphs  are  notably  different  when  the  increment  A L  is 
added  on  the  L4  side. 

Results  quite  similar  to  these  are  obtained  when  an  excess  resistance  A R 
is  used  in  place  of  A L  and  are  therefore  equally  difficult  to  construe. 

If  the  currents  i,  if  of  the  two  telephones  be  expressed  by  the  usual  equa¬ 
tions,  the  effective  current  would  be  {<p,  <pf,  phase  lags  behind  e.  m.  f.) : 

=E(cos  ip  sin  (ut—(p)/R  —  cos  <p  sin  (cot—<p')/R') 

where  cos  <£  =  A/VA2+ZAo2,  etc.,  and  the  potential  amplitude  E  of  both  is 
taken  as  equal.  This  expression  is  transferred  to 

A i=E'  sin  (co^-tan  &)/R 

which  may  be  regarded  as  the  simple  harmonic  responsible  for  the  observed 
acoustic  pressure.  Here  the  new  phase  tan  <pf  and  new  amplitude  E'  are 

tan  ^'  =  A(cos  <p  sin  <p/R)/( A  cos2  <p/R) 

E' 2  =  E*R*(( A  cos2  (p/R)2  +  (A  cos  <p  sin  <p/R)2) 

where  the  A  refers  to  differences  of  values  in  <p  and  <p',  respectively. 

When  the  two  electromotive  amplitudes  E  are  unequal,  i.  e.,  E  and  Er 
respectively,  in  circuit  T  and  T',  the  adjustment  may  be  made  by  replacing 
R'  by  R'/r. 


34 


ACOUSTIC  EXPERIMENTS  WITH  THE  PIN-HOLE 


If  the  compound  amplitude  E'  =  o,  As  =  o  results,  and  the  two  squared 
binomials  in  the  last  equation  must  each  be  zero.  Hence 

cos  <p  sin  <p/R  =  r  cos  <p'  sin  (p'/R' 

and 

cos2  (p/R  =  r  cos2  <p/R ' 

Hence  tan  (p —  tan  <pft  the  phases  are  the  same,  and  r  =  R'/R.  If  r—  i,  R'  =  R. 

Owing  to  the  asymmetric  vibration  of  plates  in  the  sequence  graph,  these 
conditions  are  further  modified.  For  small  currents  we  may  write,  as  hereto¬ 
fore,  i—s/c  and  i'  =  s'/c',  so  that  Ai  —  o  is  equivalent  to  s/c-s'/c'  —  o  or  s-s' 
would  not  be  zero. 

Without  recalling  §  23,  a  simple  method  of  procedure  would  regard  the 
minima  as  cases  in  which  the  sequence  vibrations  are  quite  in  phase  but  of 
different  amplitudes,  hence  at  the  minima  L/R  =  L'/R'  (1).  If  the  amplitudes 
are  also  equal  the  balance  is  complete.  In  this  case  the  equation 

R2+LV  =  tf,2+L'V 

again  holds,  so  that  L—L '  and  R  =  R'.  In  the  above  work,  the  inequality  of 
the  voltages  in  T  and  T'  would  have  to  be  allowed  for.  Moreover,  5  is  not 
generally  proportioned  to  the  current. 

The  L  and  R  here  treated  are  the  sum  of  internal  and  external  values. 
Calling  the  former  L0  and  R0,  the  latter  L  and  JR,  the  first  equation  is  actually 
(L-\-Lo)/(R+ R0)  =  (L'-\-L'o)/(R'-\-R'o).  If  L0,  Ro ,  are  the  same  in  the  circuits 
and  L,  R  (external)  are  initially  negligible,  Lo/Ro  =  L'/Rf,  or  a  fixed  ratio 
holds  at  the  minima.  Unfortunately,  these  conditions  are  not  here  present  and 
the  reduction  of  the  complicated  equations  does  not  seem  promising. 

27.  Same  without  commutator — To  guard  against  complications  from  a 
commutator  of  insufficiently  high  resistance,  the  commutator  C  was  excluded 
and  the  connections  made  directly  (insert,  fig.  81).  The  results  are  given  in 
figures  81,  82,  the  group  a  referring  to  a  comparison  of  external  resistances 
R'  =  0  and  R  =  o  —  4X1  o4  ohms,  only:  The  group  b  is  a  comparison  of  induc¬ 
tances  L1+L4  and  R  =  o  to  4 X  io4  ohms;  the  group  c  of  L3  and  R  =  o  to  4 X  io4 
ohms.  These  measurements  were  repeated  many  times  and  are  definite. 
Since  at  R'  =  o  and  R=  io4,  mean  5  =  64,  while  R'  =  o  and  L1+L4  gives  mean 
5=10  and  R'  =  o  and  L3  gives  mean  5  =  44,  the  inductances  would  be  of  the 
order  of  56  and  230  mh.  if  computed  linearly.  The  order  of  values  is  thus  the 
same  as  above  and  much  too  small. 

The  graphs  a  (excess  L  =  o)  differ  essentially  from  the  group  of  figure  79 
for  about  the  same  conditions.  The  two  circuits  T  (weaker)  and  V  (stronger) 
are  still  quite  unequally  efficient  (meaning  probably  that  the  coils  of  I'  and 
I "  are  not  equivalent);  nevertheless,  they  now  balance  appreciably  when 
R  =  R'  =  o  under  the  given  sensitivity.  If  R  is  added  in  the  T  circuit,  T' 
sings,  and  vice  versa.  The  tendency  to  conform  to  an  initial  minimum  is 
more  marked  in  the  lower  curve,  where  R  is  added  to  the  stronger  circuit 
T';  but  it  is  difficult  to  see  why  the  minimum  is  not  more  developed. 


PROBE  AND  THE  INTERFEROMETER  U-GAGE 


35 


In  the  graphs  b,  figure  81,  when  7^  =  0  is  replaced  by  L1+L4,  the  character 
of  the  curves,  figure  79,  is  preserved,  but  the  quantitative  divergence  is  other¬ 
wise  again  very  marked.  The  lower  graph  (fig.  816)  is  now  distinctly  hooked 
at  the  beginning  when  L\-\-L 4  is  inserted  in  T,  the  weaker  circuit;  thus  when 
the  strong  T'  is  reduced  by  R!  y  the  minimum  naturally  appears.  On  the 
other  hand,  when  L1+L4  is  inserted  in  T'}  T  is  still  less  intense  than  the 
reduced  T'  and  no  minimum  appears  in  the  upper  curve,  figure  81  b.  In  the 
hooked  graph  we  may  surmise  that  on  the  near  side  of  the  minimum  T'  sings, 
whereas  on  the  far  side  T  sings,  louder  as  R  increases. 

In  figure  82,  graphs  c ,  where  the  larger  inductance  L3  is  placed  in  one 
circuit  or  the  other,  both  graphs  exhibit  a  minimum.  In  the  upper  curve  c , 
T'  though  reduced  by  L3,  nevertheless,  is  in  excess  at  the  beginning  and 
remains  so  as  T  is  decreased  by  R.  In  the  lower  curve  c,  the  minimum  is  very 


developed,  since  T'  at  the  outset  is  much  in  excess  of  T  reduced  by  L3,  and 
higher  values  of  R'  in  Tf  are  needed  to  reduce  it  below  the  diminished  T 
value.  The  previous  minimum  at  R  below  5,000  ohms  (curve  b)  now  appears 
at  R  above  5,000  ohms.  Before  this  T’  sings,  and  after  T  is  responsible  for 
the  fringe  displacements  s. 

A  comparison  of  figure  82c  with  figure  77 b,  each  of  which  determines 
L3,  again  shows  curves  of  the  same  character  but  differing  in  detail.  Thus  the 
intersection  in  77 b  is  about  at  4X104  ohms,  whereas  in  82c  it  is  below  5,000 
ohms.  The  deep  minimum  of  the  latter  contrasts  with  the  flat  minimum  of 
the  former. 

The  minima  are  not  at  s  =  o  and  seem  to  rise  with  the  magnitude  of  L. 
In  other  words,  if  the  phases  of  the  two  telephones  are  opposed  the  amplitudes 
are  unequal,  whereas  for  equal  amplitudes  the  phases  would  not  be  opposed. 
The  curves  indicate  that  the  two  conditions  do  not  occur  together,  remem¬ 
bering,  however,  that  the  two  coils  I'  and  I"  are  unequally  efficient. 


36 


ACOUSTIC  EXPERIMENTS  WITH  THE  PIN-HOLE 


28.  Electrolytic  resistances — The  discrepancies  of  §  25  et  seq.  suggested 
a  direct  compensation  by  electrolytic  resistances  and  capacities  in  one  of  the 
circuits.  For  in  view  of  the  high  resistances  (40,000  ohms)  to  be  used  and  the 
advent  of  the  damp  summer  months,  it  seemed  not  unlikely  that  the  commu¬ 
tator  C  (fig.  75)  would  become  appreciably  leaky.  It  might  thus  be  supposed 
to  introduce  not  only  conductances  but  electrolytic  capacities,  sufficiently 
grave  to  mar  the  graphs.  The  resistances  were  made  to  favor  polarization 
and  consisted  simply  of  two  platinum  wires,  each  about  8  cm.  long,  held  about 
7  cm.  apart  in  a  beaker  of  distilled  water.  The  adjustment  is  given  in  figure 
83,  where  c  is  the  water-cell. 

The  graphs  a  of  figure  84  and  figure  83,  identical  with  the  above,  were 
obtained  with  the  short-circuited  cell  ( R0  =  o ).  The  T'  circuit  is,  as  before, 
much  the  stronger. 


The  graphs  b  of  figures  83,  84,  show  the  fringe  displacements  5  when  the 
cell  is  balanced  by  a  resistance  R.  These  graphs  immediately  recall  the  group 
in  figure  76,  where  a  similar  balance  is  made  by  metallic  resistances.  The  cell 
thus  seems  to  act  merely  as  a  resistance,  and  as  the  curves  where  5  vanishes 
indicate,  of  somewhat  in  excess  of  20,000  ohms. 

The  high  initial  ordinate  in  figure  83  as  compared  with  the  low  initial 
ordinate  in  figure  84  of  the  b  curves  are  explained  by  projecting  their  values 
horizontally  across  to  the  opposed  a  curves.  Thus,  in  figure  84,  if  R  =  o,  the 
T  telephone  sings  and  therefore  5  =  68,  in  accordance  with  figure  83  is  about 
22,000  ohms.  In  the  same  way  5  =  130  in  figure  83,  for  R  =  o,  if  interpreted  by 
the  a  curve  in  figure  84,  is  equivalent  to  23,000  ohms. 

The  curves  c  finally  give  the  data  when  the  excess  resistance  in  one  of  the 
circuits  is  R'  =  o,  and  the  variable  R  in  the  other  circuit  is  inserted  in  parallel 
with  the  cell  c.  Here  also  c  acts  as  a  parallel  resistance,  reducing  the  ordinates 
of  the  a  curves  of  figures  84  and  83  about  one-third.  When  R=  co ,  the  resistance 


PROBE  AND  THE  INTERFEROMETER  U-GAGE 


37 


of  c  is  alone  effective.  If  we  measure  each  of  the  limiting  ordinates  on  its  own 
a  curve,  the  cell  resistance  again  comes  out  a  little  larger  or  smaller  than 
20,000  ohms.  The  projections  in  question  are  indicated  on  the  diagrams. 

Thus  there  is  nothing  here  to  account  for  the  difference  of  figures  76  and 
82,  etc.  To  obtain  final  evidence,  I  tested  the  paired  connectors  of  the  com¬ 
mutator  for  c ,  figure  75,  directly,  by  removing  either  L  or  L'.  This  is  equiva¬ 
lent  to  a  break  and  should  coincide  with  R  —  °o  in  one  circuit.  The  graphs  so 
obtained  are  given  under  d ,  in  figures  84  and  83.  They  were  quite  identical, 
no  matter  whether  the  terminals  of  the  circuits  T  or  V  ended  in  the  (open) 
commutator  or  in  hard-rubber  standards.  The  commutator  had  therefore 
remained  trustworthy  and  the  cause  of  discrepancy  must  be  sought  elsewhere 

(§  29)- 


29.  Single  circuits  isolated — -The  two  curves  d  for  R'  =  co  and  R  and 
for  R'  and  R=cof  respectively,  are  themselves  interesting.  In  figure  85 
I  have  constructed  the  fringe  displacements  sT  and  sT /  obtained  at  the 
identical  resistances  marked  in  ohms  X  io3  on  the  graphs.  T'  being  more 
efficient  circuit  shows  greater  displacement,  and  the  main  part  of  the  graph 
(20,000  to  40,000  ohms)  is  so  nearly  linear  that  the  equation  =  io+i.i6st 
reproduces  the  results  very  well.  Below  R  =  20,000  there  is  increasing  curva¬ 
ture,  attributable  to  the  large  excursions  of  the  telephone-plates. 

From  this  we  get  a  definite  suggestion  as  to  the  cause  of  the  discrepancies 
in  question  and  of  the  inequality  of  circuits.  For  if  we  regard  the  induction 
(f,  f')  as  occurring  mainly  during  the  break  circuit,  and  therefore  being  uni¬ 
directional,  the  two  telephones  act  under  opposed  conditions  in  the  sequence 
adjustment.  For  while  the  plate  of  one  is  additionally  attracted,  that  of  the 
other  will  be  released,  and  it  is  quite  probable  that  these  two  impulses  will 
not  be  of  equal  intensity.  At  least,  we  would  expect  the  attraction  impulse 
to  be  stronger,  probably  at  the  ratio  1.16  just  recorded.  To  test  this,  it  is 


38 


ACOUSTIC  EXPERIMENTS  WITH  THE  PIN-HOLE 


necessary  to  reverse  both  telephones  simultaneously,  virtually  by  supplying 
two  switches  of  the  type  5  (fig.  75),  one  for  each  telephone. 

The  results  of  these  experiments  are  recorded  in  the  graphs  (figs.  86  and 
87),  which  corroborate  the  surmise,  but  provide  additional  conditions  showing 
that  the  divergence  is  much  increased  when  the  currents  in  the  circuits  are 
relatively  weak  (fig.  86)  as  compared  with  stronger  currents  (fig.  87). 

In  figure  86,  when  R  is  in  the  T  circuit,  R'  —  o,  the  T'  telephone  sounds 
strongly  in  the  upper  graph  (attraction  of  plate)  and  weakly  in  the  lower 
graph  (release  of  plate).  The  relations  are  the  same  when  Rr  is  in  the  T' 
circuit  (R  =  o)  and  T  sounds.  The  case  of  attraction  of  plate  for  T  (upper 
curve)  is  also  much  in  excess  of  the  case  of  release  (lower  curve).  It  is  inter¬ 
esting  to  note  that  T  for  an  attracted  plate  is  stronger  than  T'  for  a  released 
plate.  If  for  figure  86  we  construct  the  mean  ratio,  dsattr  /  dsreu  of  fringe 
displacements  for  attraction  and  release,  respectively,  the  results  lie  between 
2.3  and  2.0. 

The  same  interpretations  follow  from  figure  87  for  stronger  currents, 
except  that  the  two  graphs  for  T'  sounding  both  lie  above  the  graphs  for  T 
sounding,  though  the  intermediate  graphs  are  practically  coincident.  The 
graphs  for  sattr  compared  with  srei  are  here  quite  curved,  so  that  a  mean 
initial  rate  dsaltr  /dsrei  =1.5,  falling  off  to  1  near  the  middle  of  the  curves 
and  finally  to  0.7  near  to  end.  Hence  for  weak  currents  these  rates  are  about 
twice  as  large  as  for  the  strong  currents. 

The  group  of  figure  86  can  not  adequately  be  made  to  pass  into  the  graph 
of  figure  87  by  a  mere  change  of  the  scale  of  the  abscissa.  For  a  constant 
electromotive  force,  E—ir—ioro  and  a  simple  circuit,  the  equation  50  =  ser/r°  = 
selo/t  reproduced  the  observed  data  approximately.  Hence  for  two  different 
circuits  and  different  constant  electromotive  forces  and  at  the  same  external 
resistance  R  (r  =  r0  +  R\r'  =  r'o  +  R) , 


log  Sq/ s'q  —  log  s/s'  +  R  (i/r0  ~  1 /r'o) 


whence  log  s/s' =A—BR}  A  and  B  being  constants. 

On  passing  from  figure  86  to  figure  87  for  the  same  pair  of  graphs,  if  A , 
B,  R  remain  the  same 


5 


Sl 


where  Si  and  s\  are  the  new  values  of  5  and  s'. 

If  A—  log  so/s'o  and  B  =  i/ro—i/r'o  have  assumed  new  relations  in  the 
second  group, 

log  s/s'— log  S\/ s' \  —  A  — A 1  (since  B  is  constant); 


s/s'  sq/s'q 

Sl/s'i  Sqi/s'oi 


Thus  the  ratios  s/s'  vary  as  the  initial  ratio  s0/s' 0,  which  supplies  no  reason,  how¬ 
ever,  why  the  latter  should  vary,  other  than  that  these  should  approach  unity. 


PROBE  AND  THE  INTERFEROMETER  U-GAGE 


39 


30.  Data — Owing  to  the  inequality  of  electromotive  forces,  e ,  er  operat¬ 
ing  in  the  circuits  T,  T'  and  the  asymmetric  character  of  the  paired  telephone 
vibrations  in  the  sequence  adjustment,  full  computations  on  the  basis  of  the 
graphs  investigated  would  be  very  tedious  and  not  worth  while.  It  will 
suffice  to  make  a  numerical  survey  and  then  supply  a  brief  interpretation  of 
the  occurrence  of  minima  in  single  graphs  and  of  the  intersection  of  paired 
graphs. 

In  most  cases  the  telephones  T,  T’  and  the  secondaries  7,  I'  cooperated 
with  the  internal  resistances  R0,  R'0y  and  inductances  L0,  L'0  as  follows : 


Circuit  T' ,  I' 

Circuit  T,  I 

Secondary:  R0  =  31,  L0=  .39 

Telephone:  1,110,  1.2 

Total:  ^0  =  1,141  ohms,  Lo  =  1.6  henries 

Ro=  32,  Lo=  .29 

1,090,  1.2 

Ro  =  1,122  ohms,  L0  =  1.5  henries 

To  these  the  external,  R ,  L  were  added.  If  we  take  the  example  of  figure 
82,  curves  cy  with  R  in  T  andZ.3  (^  =  500  ohms,  7,3=  1.4  hen.)  in  T\  the  full 
impedances,  7,  I'  would  be: 


Circuit  T',  I' 

Circuit  T,  I 

^1  =  1,691  ohms,  Li  =  3.o  hen. 
Impedance  /' =  8,964 

Ri  =  1,122  +  R  ohms,  Li  =  i.5  hen. 

7  =  4,542,  if  R  =  0 

if  we  estimate  Li  by  its  equivalent  resistance  (Lico  =  8,800  and  4,400  ohms, 
respectively,  where  60  =  2,934).  The  same  data  applied  to  the  case  where  R' 
is  in  T '  and  L3  in  T,  give  us 


Circuit  V 

Circuit  T 

2?'i  =  1,141  +  R\  L'  =  i.6 

I’  =4,817  if  R'  =0 

Ri  =  1,670;  L  =2.9 

7  =  8,672 

after  adding  the  equivalents  of  Leo  (4,680  and  8,510). 

The  case  of  figure  81,  curves  b,  is  similarly  construed.  Here  L1+L4  adds 
resistances  of  ^  =  9.9+1.1  =  11  ohms  and  L  =  0.3 2 +0.04  =  0.36  henry.  Thus 
for  RinT and L1+L4 in  T' 


Circuit  T',  I' 

Circuit  T,  I 

R\  =  i ,  1 52  ohms ;  L\  =  2.0  henry 

Ri  =  1,122  +  R  ohms;  7i  =  1.5  henry 

or  reducing  to  ohms  roughly  as  before 

7/  =  5,982  7  =  4,541  if  R  =  o 


4 


40 


ACOUSTIC  EXPERIMENTS  WITH  THE  PIN-HOLE 


If  R'  is  in  T'  and  L1+L4  in  T,  the  case  stands 


or  briefly 


7?'i  =  1,141+7?;  L'  1  =  1.6  2?i  =  1,133 ’»  2^i  =  1.9 


I'  =  4,817  if  R  =  0  7  =  5,821 


31.  Troughs  of  the  paired  graphs — To  interpret  these  results  as  to  the 
positions  of  the  troughs,  one  may  recall  that  each  of  the  paired  graphs,  figures 
82  and  81,  is  the  superposition  of  two  individual  graphs,  one  belonging  to  the 
circuit  with  variable  R  and  the  other  to  the  parallel  circuit  with  L,  of  resist¬ 
ance  R.  The  former  (2)  decreases  regularly  with  R,  while  the  latter  (5) 
increases.  Hence  the  equations  for  parallel  coupling  will  read 

sV  (i?'  +  R’  o)2  +  LW/c’  =  {Rc  +  Rtf  +  (L  +  L„)  V/c 

if  we  postulate  roughly  i=s/c,  i'=s'/c ',  where  c  and -c'  are  the  constants 
determining  the  efficiency  of  telephones,  possibly  associated  with  unequal  coils. 

If  we  further  define  the  minimum  as  the  R'  =  R  value,  for  which  s  =  s\ 
the  latter  cancels  out,  whence 

(1)  (R'  +  R'tf  =  (j  J  ( (Rc  +  RoY  +  (L  +  Lo)V)  -  L'„V 

where  R'  is  the  position  of  the  minimum  for  the  load  L,  L0,  Ro,  Z/0,  R' 0,  are 
the  constants  (telephones  and  secondary  coils)  of  the  circuits  and  Rc  the 
resistance  of  the  load  coil  L.  On  commutation,  this  equation  becomes 

(2)  (R  +  R0y  =  L  (  (Rc  +  R'oY  +  (V  +  L'„)V)  -  LoV 

c 

where  R  is  the  position  of  the  minimum  for  the  load  L'  =  L  in  the  parallel 
circuit. 

If  the  inherent  constants  L0,  L'0,  2?o,  R'o ,  are  nearly  the  same  and  if  c  =  c'} 
nearly,  since  L  =  L',  equations  (1)  and  (2)  are  identical  and  R  =  R'.  This 
means  that  the  paired  graphs  of  figures  82,  81,  must  coincide  and  there  is  but 
one  minimum.  If,  however,  c/cf>  1  then  c'/c  <  1,  from  which  the  occurrence 
of  separated  paired  graphs,  each  with  its  own  minimum,  results.  The  equa¬ 
tions  show,  moreover,  that  R  will  be  larger  as  L'  is  larger,  conformably  with 
the  graphs  investigated. 

Equations  (1)  and  (2),  however,  suffice  for  the  elimination  of  c/c',  if  they 
are  multiplied  together,  so  that  the  geometric  mean  is  really  in  question  in 
relation  to  R,  and  R\  the  positions  of  the  troughs. 

If  we  now  use  the  data  of  paragraph  30,  given  for  the  circuit  Li+Z,4  = 
L  =  L',  we  obtain 

(R'  +  i,i4i)2  =  (c'A)2(i,i332  +  (2  .oco)2)  (1 .6co)2 

and 

(R  +  I,I22)2=  (c/c')2(i,I522  +  (2.OC0)2)  —  (i.6co)2 
whence  if  c/c'  =  1,  R'  =  2,560  ohms  and  R  =  2,550  ohms,  a  mean  value. 


PROBE  AND  THE  INTERFEROMETER  U-GAGE 


41 


If  the  former  datum  c/c'  — 1.2  or  (c/c')2  —  1.4  be  taken,  R'  =  720  ohms  and 
7?  =  4, 170  ohms  results.  These  data  agree  reasonably  well  with  the  graphs 
figure  8 1 ,  although  the  c/c'  found  for  the  old  telephones  is  here  merely  tentative. 
The  constants  for  the  circuit  L3  give  us 

( R '  +  i,I4i)2  =  (c'A)2(i,6222  +  (3.OCJ)2)  —  (i.6a>)2 

and 

(R  +  i,i22)2=(c/c')2(i,64i2  +  (3.0a?)2)  — (i.6co)2 

whence  if  c/c'  —  1,  R' =  6,480  ohms  and  R  =  6, 500  ohms,  a  good  mean  value 
for  the  position  of  the  minimum,  if  the  graphs  coincide.  If  (c/c')2  =  1.4.  as 
above,  ^'  =  4,790  ohms  and  R  =  8,375  ohms,  which  are  both  somewhat  high, 
showing  that  for  large  inductances  like  L3,  the  insufficiency  of  the  approxima¬ 
tions  imposed  is  perceptible. 

Moreover,  in  all  cases,  if  the  minimum  R  were  sharply  determined,  L 
would  follow  by  an  inverse  computation. 

In  equation  (1)  or  (2)  ifL  denotes  the  inductance  of  the  coil  only  (uncored) 
and  if  this  is  small  compared  with  Lq  =  L'0,  the  equations  become,  since  R'o  =  Ro 

(R'  +  R'oY  =  (c'/c)2(Rq  +  Rc)2  +  U V((c'A)2  - 1) 

If  c'  =  c ,  then  R'  =  Rc.  Thus  the  resistance  position  of  the  minimum  R'  for 
the  uncored  coil,  gives  its  resistance.  Equation  (1)  for  the  cored  coil  takes 
the  form  ( c  =  c'),  since  Rc  is  now  given 

(R'  +  RC+  2  Rq)  (R'  Rc)  =  (L+  2L0)Lco2 

where  R'  is  now  the  position  of  the  minimum  for  cored  coil,  L.  These  two 
operations  suffice  to  determine  L;  hence  it  is  obvious  that  the  desideratum 
c  =  c'  must  be  secured  as  nearly  as  possible  in  any  efficient  apparatus. 

We  may,  however,  eliminate  c  and  c'  by  rewriting  equations  (1)  and  (2) 
with  these  coefficients  and  multiplying  the  equations  together.  Since  L0  = 
L' 0  and  Ro  =  R'o  this  gives 

(Rc  +  i?0)2  +  (L  +  Lo)V=V(  (R'  +  R,)*  +  LoV)(  (R  +  R,)2  +  W) 

where  R  and  R'  are  the  observed  minima  and  Rc  the  coil  resistance  of  L. 
If  L  (uncored)  is  small  compared  with  Lq,  Rc  is  determined  from  R'  and  R  in  a 
first  operation.  With  Rc  given,  L  (cored)  is  then  determined  from  R  and  R' 
for  the  complete  coil. 

32.  The  intersection  of  paired  graphs — If  we  treat  the  present  experi¬ 
ments  in  which  the  currents  in  the  T ,  T'  circuits  are  coupled  by  mutual 
induction  as  if  they  were  ordinary  currents  in  parallel,  the  results  are  a  close 
approach  to  the  actual  case.  The  later  data  of  figures  82  and  81  are  available 
for  testing  the  case  by  computing  R  for  the  points  at  I,  at  which  the  graphs 


42 


ACOUSTIC  EXPERIMENTS  WITH  THE  PIN-HOLE 


b  and  c  intersect.  The  equation  for  the  purpose  has  been  given  (A s  =  As')  in 
§36  and  may  here  be  put  in  the  form,  if  i=s/c,  etc., 


+ 


V  (R'  +  R'o)2  +  L'0V  V(R  +  Ro¥ + LoV 

cf  c 


+ 


V(R' 0  +  Rx)2  +  (L*  +  L’ o)V  V(Ro  +  Rxy  +  (Lx  +  Lo)  V 


Here  Rx  and  Lx  are  the  resistance  and  inductance  of  the  coil  commutated  and 
R'  =  R  are  the  observed  resistance  at  the  point  of  intersection.  Ro,  Lo,  R'o ,  L'o 
are  the  constants  of  the  secondaries  and  telephones  as  indicated  in  figure  82. 
The  data  are  (0  =  2,934) 


Telephones:  T',  i?'0  =  1,1 10;  £0  =  1.2 
Secondaries:  I',  30  .4 

Total:  ^'0  =  1,140  ohms;  £0  =  1.6  henries 


T,  R0  =  T,ogo;  £0  =  1.2 

L  32  .3 

Total  =  1,122  ohms;  £0  =  1.5  henries 


These  values  are  nearly  enough  alike  for  the  T  and  T'  circuits  that  a  mean 
may  be  taken  with  the  object  of  simplifying  the  cumbersome  equation  just 
stated.  This  reduces,  if  Lo  =  L'0,  Ro  =  R'o,  and  R'=R  at  the  intersectionTo 

(R  +  Rq)2—(Rx  +  Ro)2  +  {(Lx  +  LoY—Ld 2 }  co2 

If  now  Rx,  Lx  refer  to  the  coils  L1+L4  of  the  graph  b ,  figure  81,  Rx—  1 1  and 
Lx=. 36,  so  that 

(R- f-  i,i3i)2  =  (i,i42)2+  ((i.96)2-(i.6)2)co2 

from  which  R  =  2,380  ohms.  The  point  of  intersection  in  figure  64 b  is  at  about 
2,000  ohms. 

If  Rx,  Lx  refer  to  the  coil  L3  of  graph  c ,  figure  82, 1^  =  550  ohms,  L3=  1.4 
henries,  whence 

(R+  i,i3i)2  =  (i,68i)2+  ((3.o)2-(i.6)2)co2 

from  which  7?  =  6,511  ohms,  while  the  point  of  intersection  in  figure  82c  is 
between  4,000  and  5,000  ohms. 

In  both  cases,  therefore,  the  computed  point  of  intersection  lies  above  the 
point  given  by  the  graphs;  but  the  order  of  values  is  very  satisfactory,  as  one 
can  not  expect  sharp  values  from  the  approximate  current  equations  i  =  s/c 
and  i'—s'/c ',  postulated.  Moreover,  the  same  equations  have  been  made  to 
include  the  inequalities  of  induction  e,  e'.  The  equation  for  (R+R0)2, 
moreover,  shows  in  general  that  the  point  of  intersection  of  the  paired  curves 
moves  to  the  right  both  with  Rx  and  Lx  of  the  commutated  coils. 

If  we  reverse  the  process  and  compute  Lx  from  the  intersections,  R  =  2,000 
and  4,500  of  the  graphs,  the  data  come  out  Lx  —  0.28  and  1.03  henries,  respec¬ 
tively.  This  is  0.28/0.36  =  0.78  and  1.03/1.40  =  0.74  of  the  actual  value;  or 
on  the  average  the  results  obtained  from  intersections  are  24  per  cent  too 
small. 


PROBE  AND  THE  INTERFEROMETER  U-GAGE 


43 


33.  Parallel  circuits  actuated  by  single  inductor  open  circuits — Owing  to 
the  effective  inequality  of  the  secondaries,  certain  complications  are  intro¬ 
duced  in  the  preceding  paragraphs,  which  may  be  avoided  (apparently)  by 
using  a  single  inductor  with  the  circuits  in  parallel.  Figure  88  gives  a  diagram 
of  the  connections.  Here  P  is  the  primary,  with  the  electromotive  force  E 
(3  cells  with  20  or  more  ohms  resistance)  and  B  the  periodic  break.  The 
coaxial  secondaries  I  and  I'  terminate  in  the  clamps  1,  2,  3,  4,  which,  when 
joined  at  2,  3,  produce  a  single  secondary.  Either  coil  may  be  used  alone,  the 
two  joined  in  parallel,  or  even  differentially,  in  the  usual  way.  The  parallel 
circuits  are  branched  from  the  switch  5,  which  admits  of  the  reversal  of  the 
current  in  one  of  the  telephones  (T).  The  two  telephones  T,  T'  are  joined  by 
the  acoustic  pipe  tt  with  its  salient  and  reentrant  pin-hole  probes  s ,  r,  and  the 
interferometer  U-gage  lies  beyond  U.  The  four  terminals  of  these  high- 
resistance  telephones  end  on  one  side  of  the  commutator  K ,  already  described 
in  figure  57.  By  the  aid  of  it,  the  external  resistances  and  inductances  R,  L, 


R'r  L'  may  be  inserted  in  either  one  telephone  or  the  other  by  swiveling  the 
bars  of  K,  as  indicated  by  the  dotted  lines.  Capacities  are  inserted  at  pleasure 
between  clamps  2,  3. 

On  trying  out  this  arrangement  with  I  and  I'  joined,  it  was  astonishing  to 
find  an  extremely  low  sensitiveness  compared  with  the  preceding  results, 
other  things  being  the  same.  Figures  89  and  90  (sequence-graphs)  give  the 
results  (2  cells,  10  ohms  in  the  primary).  The  inset  shows  that  the  clamps  2 
and  3  are  joined  and  the  secondaries  J,  I'  in  series.  In  figure  89  the  branch 
circuits  from  S  contain  the  telephone  inductances  only.  The  external  resist¬ 
ance  of  one  circuit  is  left  at  zero,  while  that  of  the  other  is  increased  from 
R  =  o  to  4  X  io4  ohms.  In  figure  90,  the  external  inductance  L  =  1.4  henry  and 
R  =  SS o  ohms  is  added  to  the  constant  circuit.  The  feeble  fringe  displace¬ 
ments  s  obtained  in  both  cases  are  clearly  evidenced  when  their  figures  are 
compared  with  figure  82,  for  instance,  where  the  same  routine  is  followed. 
The  character  of  corresponding  figures,  however,  is  otherwise  the  same, 
except  that  the  efficiency  of  telephones  happens  to  be  reversed.  In  figure  90, 
for  instance,  while  the  graph  for  one  telephone  ( T R  in  T)  contains  a  marked 
trough,  the  other  does  not. 


44 


ACOUSTIC  EXPERIMENTS  WITH  THE  PIN-HOLE 


To  ascertain  the  reason  for  this  behavior,  half-coils  7,  7'  (secondaries) 
were  joined  in  different  ways,  with  the  results  summarized  in  the  following 
schedule.  The  numbers  refer  to  the  terminals  in  figure  88  and  5  is  the  cor¬ 
responding  fringe  displacement  observed  (2  cells,  10  ohms)  in  the  primary 
and  R  =  o,  R'  =  3  X  io4  ohms  excess  resistance  in  the  secondary  7,  I'. 


Terminals  'used 

Terminals 

joined 

Terminals 

open 

s 

Remarks 

Closed  circuits:  1,  2 

1 

1 

2 

Open  circuits:  1 

2 

1 

3 

3,4 

4 

3 

4 

4 

3 

2 

4 

it  2  ;  3,  4 

3 ;  2 

•  •  •  • 

•  •  •  • 

2  ;  4 

1  ;3 

3  ;  2 

1  54 

3  ;4 

1  ;  2 

26 

39 

57 

65 

70 

56 

0 

0 

Coils  7, 1',  in  parallel 
Coils  I,  If,  in  series 

>  Single  coils 

\  Terminals  in  phase; 

/  or  opposite  potential 
Terminals  in  opposite 

►  phases  or  same  po¬ 
tential 

These  data  are  further  exhibited  in  figure  91.  7,  7'  in  parallel  (ohmic 
resistance  15  ohms)  constitute  the  worst  adjustment.  7, 1'  in  series  (resistance 
60  ohms)  is  better,  but  much  inferior  to  the  single  coil  7  or  7'  (resistance  30 
ohms)  used  alone.  These  again  are  less  sensitive  than  an  open  arrangement 
in  series),  i.  e.,  where  the  clamps  2,  3  are  not  joined  if  1,  4  are  the  terminals  and 
vice  versa.  If  the  coils  7,  I'  are  open  and  reversed  (i.  e.,  1,  2  terminals  and  3, 
4  free)  the  differential  effect  is  practically  5  =  0.  The  reason  for  this  is  not 
at  once  evident;  but  the  data  show  that  when  clamps  2  and  3  are  not  joined, 
the  highest  potential  difference  will  be  brought  to  the  clamps  a,  c  of  the 
switch  5,  figures  92  and  93.  There  is  a  partition  of  the  energy  of  each  impulse 
of  the  primary,  the  external  circuit  receiving  a  maximum  when  least  is  ab¬ 
sorbed  by  the  secondary.  Thus  the  electromotive  force,  E,  in  an  ohmic  coil 
resistance  of  30  ohms,  is  more  efficient  than  E  in  a  resistance  15  ohms,  or 
than  2 E  in  a  resistance  of  60  ohms. 

Figure  94  gives  a  record  of  the  effect  of  exchanging  the  clamps  1,  4  into 
4,  1  with  2,  3  open;  and  of  2,  3  into  3,  2  with  1,  4  open,  when  R  =  3  Xio4  ohms 
is  put  in  the  T  circuit  and  R  =  o  in  the  T'  circuit.  These  5  data  may  be  arranged 
thus: 

(1,  4)  (4*  1) 

5  =  114  5=90(2,3) 

72  74  (3,  2) 

Since  the  resistance  3X104  ohms  in  the  T  circuit  virtually  removes  this 
telephone,  so  that  in  the  sequence  adjustment  Tf  only  sings,  the  exchange  of 
the  terminals  1,  4  into  4,  1  is  equivalent  to  a  commutation  of  the  current  in  the 
telephone  whereby  the  stronger  inductive  impulse  is  replaced  by  the  weaker. 
The  same  is  true  for  the  change  of  2,  3  into  3,  2.  On  the  other  hand,  the 
passage  of  the  terminals  from  1,  4  to  2,  3  is  equivalent  to  a  commutation  of  the 
induction  coils  7  and  7',  which  are  not  equal,  as  shown  above.  Hence  in  1,  4, 
2,  3,  the  strong  phase  of  the  telephone  is  associated  with  the  stronger  coil, 


PROBE  AND  THE  INTERFEROMETER  U-GAGE 


45 


whereas  in  4,  1,  3,  2,  the  weaker  phase  is  associated  with  the  weaker  coil, 
as  suggested  by  the  schedule. 

Figure  92  was  obtained  with  the  favorable  arrangement  shown  in  the 
inset,  figure  93,  2,3  open.  The  graphs  are  a  considerable  improvement  on 
the  corresponding  results  in  figures  89  and  90,  of  which  they  reproduce  the 
general  character.  One  notes  that  both  for  L  =  o  and  L  =  L3  the  graphs  are 
relatively  much  nearer  together.  Two  cells  and  10  ohms  were  in  the  primary. 


In  figure  95,  the  fringe  displacement  is  further  increased  by  using  3  cells 
and  20  ohms  in  the  primary,  and  this  enhancement  might  have  been  increased 
indefinitely.  In  figure  95,  however,  the  graphs  for  L  —  o  are  reversed  and 
those  for  L3  intersect  at  high  resistance  of  about  jR  =  2Xio4,  as  compared 
with  R  =  2  X  io3  of  figure  92.  Since  these  departures  are  due  to  the  telephone 
only,  they  are  not  susprising  after  the  investigations  made  in  the  earlier  par¬ 
agraphs.  With  a  perfectly  symmetrical  telephone,  there  would  be  but  one 
curve  for  each  L.  The  location  of  minima  in  figures  92  and  95  is  about  the 
same. 

34.  Minima  and  intersections — If  we  make  use  of  the  equation  in  para¬ 
graph  3 1  for  the  R- location  of  the  troughs  and  put  c/c'  —  1  for  the  mean  value 
(w  =  2,934),  the  result  is: 

( R  +  I,IOo)2  =  {  (550  +  I ,  IOo)2  +  (1.4  +  I.2)  2C02  I  — (i.2)2£02 
or  R  =  5,870  ohms. 

Here  the  constants  (R  =  R'0  =  1,100  ohms,  Rc  —  550  ohms,  Lq  =  L'q  =  1.2 
henries,  L=Lc=i.4  henries)  have  been  used,  as  already  defined,  and  the 
equation  is  more  fully  guaranteed,  since  the  circuits  in  question  are  actually 
in  parallel.  The  R-v alue  found  is  again  somewhat  in  excess  of  the  mean 
position  of  the  troughs  in  figures  92  and  95,  owing,  no  doubt,  to  the  approxima¬ 
tions  necessarily  made  and  the  flatness  of  the  troughs.  One  notices  that  in 
figure  90,  as  in  figure  82,  one  of  the  pairs  of  graphs  for  the  case  of  L3  is  without 
a  trough,  for  reasons  which  are  difficult  to  disentangle. 

In  figures  90  and  82,  moreover,  the  intersections  of  the  L3  graphs,  like  the 


46 


ACOUSTIC  EXPERIMENTS  WITH  THE  PIN-HOLE 


troughs,  have  about  the  same  ^-location,  these  cases  corresponding  to  closed 
circuits.  In  figures  92  and  95,  however  (open  circuits),  the  paired  troughs 
(and  particularly  the  enormously  displaced  intersection)  are  virtually  new 
phenomena.  The  intersections  lie  at  about  R=  1,000  and  R  =  24,000  ohms, 
respectively.  This  is  beyond  the  range  of  approximations  (current,  i—s/c, 
etc.)  tentatively  adopted.  While  in  figure  95  the  R  in  T'  graph  has  merely 
been  raised,  as  compared  with  figure  92,  the  R  in  T  graph  has  been  raised  and 
accelerated. 

35.  Resistances  in  the  air-gap  2,  3.  Double  symmetrical  inductor — In 

figure  96,  curve  a  (insert)  where  I  and  I'  are  the  secondaries  and  T  and  T' 
the  telephones,  a  resistance  R  was  put  across  the  otherwise  open  clamps  2,3. 
The  telephone  T'  was  left  without  external  resistance  and  30,000  ohms  inserted 


in  the  branch  T ,  which  nearly  cuts  it  out.  The  fringe  displacements  s,  ob¬ 
served  as  R  increases  from  o  to  <»  ohms,  are  well  shown  by  the  graph.  It 
will  be  seen  that  5  is  more  than  doubled  by  this  procedure;  but  the  A-effect 
increases  very  rapidly  and  a  resistance  of  a  few  thousand  ohms  suffices  to 
bring  out  nearly  the  whole  of  the  displacement.  When  R  =  o,  the  internal 
resistances  are  about  31  ohms  in  each  half-coil  and  1,100  ohms  in  the  telephone 
T'.  At  R  =  io3  ohms,  however,  the  reciprocation  between  I  and  V  is  only 
about  half  quenched.  As  the  capacity  of  the  open  circuit  is  not  known,  it  is  of 
interest  to  introduce  an  external  capacity  at  2,  3.  This  will  be  done  in  the 
next  paragraph. 

Figure  96,  curve  b ,  is  another  survey,  made  with  a  somewhat  modified 
circuit,  some  time  after.  The  graphs  are  of  the  same  nature,  the  second 
having  somewhat  larger  coefficients.  It  would  be  an  advantage  to  cut  out 
the  telephone  T  altogether. 


CHAPTER  II 


SHORT  AND  SLENDER  AIR-COLUMNS.  CIRCUITS  WITH  LOCALIZED 

CAPACITY 

36.  Capacities  in  the  air-gap — It  is  thus  becoming  more  and  more  evident 
that  the  conditions  of  an  electric  circuit,  oscillating  in  resonance  with  the 
acoustic  pipe  (which  measures  s),  are  being  approached.  Hence  a  variable 
capacity  was  inserted  at  C  between  the  secondary  coils  I  and  V  as  shown  in 
the  insert,  figure  97.  T'  is  the  telephone  actuating  the  pipe;  the  other  tele¬ 
phone,  T,  being  cut  out  from  action,  its  plate  serves  merely  as  a  wall  for  the 
reflection  of  sound.  P  is  the  primary  with  electromotive  force  E  (3  cells  and 
20  ohms)  and  B  the  periodic  break.  The  results  obtained  when  the  capacity 
added  increases  in  steps  of  0.1  microfarad  from  o  to  °°,  are  shown  by  the 
graphs  a,  b ,  c,  for  somewhat  different  adjustments  as  to  sensitiveness  and 
made  at  different  times.  The  full  capacity  is  now  C+Co,  where  C  is  the  capac¬ 
ity  of  coils  I,  I',  here  (in  the  apparatus)  forming  a  coaxial  structure  favorable 
to  capacity.  Thus,  the  fringe  displacement  5  begins  in  marked  degree  when 
C  =  o.  If  one  of  the  layers  is  replaced  by  a  similar  but  remote  coil,  there  is  no 
fringe  displacement  (5  =  o)  at  C=  o. 

The  curves  are  seen  to  be  of  the  same  nature,  and  all  insist  on  a  maximum 
somewhat  below  0.05  microfarad,  the  smallest  standard  interval  here  available. 
The  curves,  moreover,  pass  through  a  definite  minimum  at  about  0.5  micro¬ 
farad  of  added  capacity.  This  has  been  worked  out  in  greater  detail  in  the 
graph  d.  At  C  —  1  microfarad,  the  graphs  have  practically  reached  the  limit, 
as  shown  in  case  of  the  curve  c  when  the  condenser  C  is  short-circuited.  At 
times  there  seemed  to  be  an  actual  maximum  near  C=  1  microfarad  possibly 
referable  to  the  primary;  but  this  was  obscure  and  not  borne  out.  Thus  there 
is  no  doubt  that  the  initial  sharp  maximum  is  due  to  electric  oscillation.  To 
compute  its  position  in  C,  the  usual  equations 

T  —  2TT  \/ LC  y/ 1  +  ( d / 27 r)2 
where  d  is  the  logarithmic  decrement 

d  =  RT/2L 

are  available.  The  total  resistance  of  telephone  and  coils  is  (as  above), 
R=  1,100  +  62  =  1,162  ohms  and  the  total L=  1.55  henries.  From  this  d  =  0.65, 
the  frequency  of  W  being  467  or  <0  =  2,934,  co2  =  io6  X  8.61.  Hence  d/ 27r  =  0.104 
and  (d/271-)2  =  0.011.  Equation  (1)  may  therefore  be  written 

C=  i/(Lco2(i  +  (d/271-)2)  =0.365.  microfarad 

As  this  is  Cc-\-Co  the  external  and  inherent  capacity,  Cc  —  0.365  —  Co,  which 
might  be  regarded  as  the  C-location  suggested  by  the  graphs.  Since  the 
mutual  inductance  has  been  disregarded,  L  is  virtually  larger,  and  hence  Cc 

47 


48 


ACOUSTIC  EXPERIMENTS  WITH  THE  PIN-HOLE 


should  be  smaller  still.  The  meager  effect  of  d,  in  consideration  of  the  large 
resistances,  is  noteworthy;  but  the  crests  are  nevertheless  flattened  as  a 
consequence. 

The  minimum  at  £  =  0.5  microfarad  is  more  difficult  to  construe,  for  here 
the  electric  oscillation  is  nearly  quenched  and  the  telephone  acoustically 
silent.  As  67  alone  varies  from  its  initial  value  67r  for  resonance,  T/T0  =  '\^C/Cr. 
Hence  "\/67/o.o36  =  2,  or  67  =  0.15  mf.  if  the  initial  period  W  were  doubled  and 
\/ 67/. 036  =  3  or  67  =  0.33  mf.,  if  this  period  were  trebled;  67  =  0.58,  if  quad¬ 
rupled,  etc.  Nothing  seems  to  occur  at  T/Tq  —  2,  or  =  3,  or  =  4  with  any 
bearing  on  the  problem. 


Both  telephones  T  and  T'  may  be  used  to  advantage  as  in  figure  98, 
provided  the  telephones  vibrate  in  phase.  This  nearly  doubles  the  sensitive¬ 
ness,  so  that  the  primary  current  must  be  weakened  (3  cells,  50  ohms)  if  the 
fringes  are  to  remain  in  the  field  of  view.  Considerable,  difficulty  was  experi¬ 
enced  with  the  break  in  the  primary,  which  when  freshly  polished  with 
slightly  oiled  paper  gave  higher  5-values  than  appeared  shortly  after;  but  the 
sinuous  character  of  the  curves  in  figure  9 8,  a  and  b ,  is  nevertheless  warranted. 
The  crests  in  figure  98,  a,  b  are  not  sharp.  They  might  suggest  a  subsidiary 
crest  at  about  67  =  0.25.  The  minimum,  moreover,  has  moved  to  the  left  and 
would  be  expected  beyond  67  =  0.5.  Curves,  figure  98,  c  and  d,  were  also 
sometimes  obtained,  rising  above  the  crest  of  b,  nevertheless,  falling  as  low  as 
a  and  without  the  retardation  at  67  =  0.2  of  curves  a  and  b\  so  that  an  unstable 
situation  is  involved.  The  constants  being  practically  the  same  as  the  above, 
computed  data  would  also  be. 


PROBE  AND  THE  INTERFEROMETER  U-GAGE 


49 


37.  Single  inductor,  unsymmetrical — The  case  of  C=  »  (short  circuit) 
in  figure  98 b  has  the  low  value  already  instanced  in  paragraph  33,  for  the 
symmetrical  circuit  using  7  and  I'.  In  figure  99,  a,  b ,  c ,  the  counter  cases  are 
shown  in  which  either  I  or  I'  alone  are  the  secondaries  of  the  inductor.  In 
curves  a  and  b  (see  insert),  but  one  telephone  is  used,  the  silent  plate  of  the 
other  merely  reflecting  the  sound-wave.  In  curve  c  the  two  telephones  are 
used  in  parallel  and  in  phase.  The  latter  is  naturally  over  twice  as  sensitive, 
owing  to  the  decreased  resistance;  so  that  3  cells  with  20  ohms  were  used  in 
the  former  primary  and  3  cells  with  50  ohms  in  the  latter. 

The  graphs  obtained  in  figure  99,  a,  b,  c ,  are  quite  different  from  the  set  in 
figure  98,  for  the  symmetrical  arrangement.  Thus  at  C=  00  the  currents  5  are 
still  very  high,  relatively  speaking,  and  also  in  conformity  with  the  informa¬ 
tion  in  paragraph  33.  There  is  no  appreciable  current  (5  =  0)  when  the  added 
capacity  is  C  =  o.  At  C  =  0.05,  the  current  at  once  jumps  beyond  the  maximum 
and  falls  but  slightly  thereafter 
(C  =  o.i  to  1.0).  There  is  no 
minimum  determinable.  Since 
the  resistance  of  the  telephones  120 
T  and  T'  is  large  as  compared 
with  the  secondaries  7  and  I',  100 
the  use  of  the  latter  singly  or 
together  would  not  make  much 
difference  (1,100+62  ohms  com-  qq 
pared  with  1,100+31  ohms; 
with  the  telephones  in  parallel  42 
550+62  and  550+31).  The 
currents  change  from  s  =  40  in  20 
figure  98,  to  5  =  85  to  100  in  fig¬ 
ure  99  when  C=  co  f  and  the  data  ^ 
are  similar  relatively  to  figure 
97.  The  released  resistance  may  therefore  be  the  mutual  induction  in  the  coils 
7,  7',  which  is  cut  down  one-half  or  proportionally  and  to  which  no  adequate 
reference  has  been  made.  The  curves,  in  fact,  are  quite  similar  to  the  graphs 
usually  obtained  in  case  of  closely  coupled  circuits  of  primary  and  secondary 
and  the  treatment  would  be  conducted  along  similar  lines  to  those  usually 
pursued. 

The  absence  of  all  fringe  displacement  (5  =  0)  when  C  =  o  implies  that 
the  inherent  capacity  is  virtually  C0  —  o  in  case  of  the  single  coil ;  whereas  the 
combined  coils  7,  I'  owe  their  marked  inherent  capacity  to  their  coaxial 
arrangement. 

At  a  later  date  capacities  between  o  and  0.1  microfarad  in  steps  of  0.0 1 
microfarad  were  procured  and  the  graphs  d  and  e  in  figure  99  worked  out  at  a 
somewhat  larger  current  intensity.  In  the  higher  curve  e ,  the  pitch  was  reset 
for  the  maximum  at  each  observation;  in  curve  d  the  motor  was  kept  running 
at  the  maximum  for  the  pitch  at  (7=0.5. 


50 


ACOUSTIC  EXPERIMENTS  WITH  THE  PIN-HOLE 


The  crest  now  lies  definitely  nearest  £  =  0.03  microfarad.  Since  for  the 
primary  00  =  2,934,  it  is  worth  while  to  compute  the  effective  inductance, 

including  self  and  mutual  inductance  in  the  form  1  =  o>\ / (L  +  Li2)C.  The 
result  is  L  +  Ln  =  3.9  henry ;  so  that  if  for  I  and  T  +  T'  L  =  0.8  henry,  Li2  =  3.1 
henry  would  be  estimated  (C0  =  o,  as  stated).  As  this  is  out  of  the  question, 
it  looks  as  if  the  harmonic  were  not  b'  but  b" .  The  fringe  displacements  of  the 
graphs  d,  e,  figure  99,  were  liable  to  pass  out  of  the  field  of  the  ocular.  A 
larger  resistance  was,  therefore,  inserted  into  the  primary  (3  cells,  60  ohms)  to 
bring  the  currents  within  the  scale  limits.  The  results  are  given  in  figure  100. 
The  enlarged  curves  b ,  c  are  constructed  with  a  AC  =  0.01  microfarad  interval. 
The  general  trend  of  the  curves  is  much  the  same  and  for  the  C  =  o.i  micro¬ 
farad  interval  the  graphs  now  come  out  sharply  with  a  maximum  at 
about  0.025  microfarad.  In  the  graph  b,  the  primary  pitch  W  was  set  and  the 
successive  points  investigated  by  changing  C  in  steps  of  0.01  microfarad.  In 


the  graph  c ,  however,  the  maximum  5  was  sought  at  each  C,  by  changing  the 
frequency.  The  result  was  not  only  a  larger  5  throughout,  but  the  maxima 
of  5  were  found  at  slightly  higher  pitch  for  a  smaller  C.  This  is  indicated  by 
the  insert  d,  where  at  C  =  o.o2  microfarad  and  a  pitch  a  little  below  b',  the 
deflection  was  5=120,  falling  to  93  at  W\  while  at  C  =  o.o3  microfarad  the 
deflection  was  but  5  =  95  at  bf,  rising  to  125  at  W,  the  pitch  difference  being  a 
diminished  semitone.  These  alternative  crests  are  not  uncommon ;  but  it  is  not 

easy  to  assign  the  cause,  except  in  so  far  as  in  1  =  27 rnwLC  a  reciprocal  change 

of  n  and  V C  does  not  change  the  product  and  is  admissible  within  the  reso¬ 
nance  limits  of  the  acoustic  pipe  joining  the  telephones.  As  in  the  insert, 
however,  there  is  always  a  maximum  among  the  crests,  here  at  W.  Cases  as 
low  as  a'  were  observed  in  other  instances. 

In  figure  101,  one  telephone  (T)  is  cut  out  of  circuit  and  is  inactive,  the 
sound-wave  from  T'  being  merely  reflected  at  the  plate  of  T.  Three  cells 
and  30  ohms  were  therefore  used  in  the  primary.  The  interval  o  to  0.1  micro¬ 
farad  is  here  mapped  out  in  steps  of  0.01  microfarad  not  available  in  figure  99. 


PROBE  AND  THE  INTERFEROMETER  U-GAGE 


51 


i 

An  interesting  new  feature  is  the  occurrence  of  two  crests  seen  in  curve  a 
(interval  AC  =  o.oi  microfarad),  but  more  sharply  in  curve  b  (AC  =  o.i  micro¬ 
farad).  This  is  unexpected,  as  only  one  telephone  is  in  action;  but  the  double 
crest  probably  presents  an  adventitiously  indented  form  of  a  single  crest,  as 
indicated  by  the  dotted  lines.  In  fact,  in  subsequent  experiments  the  double 
crest  did  not  always  appear,  so  that  it  is  incidental  and  (7  =  0.055  would  mean 
L  =  0.53  hen.  not  identifiable. 

38.  Effect  of  the  lower  harmonics — Figure  102  is  an  attempt  to  work 
out  the  character  of  the  flat  crest  of  figure  97  in  greater  detail  (curve  a  with 
steps  of  0.01  microfarad);  but  it  presents  no  essential  novelty.  The  high  5 
for  C  =  o  is  again  attributable  to  the  capacity  of  the  coaxial  double  coil  I,  I'. 
Details  at  the  minimum  were  supplied  at  a  later  date  in  curve  c. 


The  same  is  true  of  the  repetition,  figure  103,  in  relation  to  figure  98, 
for  the  primary  pitch  b&'.  There  is  initial  capacity.  The  attempt  was  then 
made  to  use  the  node  of  a  lower  (apparent)  harmonic  of  the  organ-pipe,  as  it 
was  possible  to  isolate  a  strong  one  near  d'  for  the  primary  by  slowing  up  the 
break.  The  lower  graph  in  figure  103  gives  the  results,  which  indicate  a  shift 
of  the  crest  to  the  right  (which  would  be  expected)  and  the  occurrence  of  a 
probable  very  flat  maximum  beyond  the  minimum.  The  latter  is  necessarily 
uncertain  in  view  of  the  small  s- values  remaining.  The  shift  in  the  former  case, 
moreover,  is  hardly  adequate.  Since  nothing  is  changed  but  the  primary 
pitch  from  W  to  d\  we  have 


=  0.40 


52 


ACOUSTIC  EXPERIMENTS  WITH  THE  PIN-HOLE 


In  figure  103,  if  the  crest  at  W  is  at  C  =  o.o7  microfarad,  the  crest  at  d! 
should  be  at  C'  =  o.o7/(o.4)  =0.18  microfarad,  at  least,  since  initial  capacity  is 
not  easily  estimated.  Though  the  figure  may  so  be  drawn,  it  is  not  convincing. 

It  is  thus  preferable  to  work  with  the  unsymmetric  adjustment,  figure  104 
(compare  figure  100),  which  has  no  initial  capacity.  The  results  are  given  in 
the  two  graphs  of  the  figure,  in  the  upper  one,  a,  of  which  the  resonance  was 
tested  at  each  point.  They  contain  the  new  feature  of  two  distinct  or  separate 
peaks.  The  first  at  about  £7  =  0.03  microfarad,  nearly  coincides  with  the  peak 
in  figure  100,  and  would  thus  be  associated  with  the  primary  W  pitch.  The 
other  at  C  =  o.i7  microfarad  is  new  and  should  therefore  be  referred  to  the 
present  primary  d'  pitch. 

To  account  for  the  presence  of  both  crests  it  would  seem  reasonable  to 
refer  the  latter  to  the  actual  period  of  the  spark  succession  at  the  break  in 
the  primary.  The  former  would  then  be  due  to  an  electrical  oscillation 
sustained  between  sparks,  which  happens  to  be  in  resonance  with  the 
acoustic  note  W  of  the  pipe  joining  the  telephones.  In  other  words, 
although  the  spark  succession  corresponds  to  df,  an  electric  oscillation  W 
will  nevertheless  evoke  this  natural  note  of  the  pipe,  owing  to  accentuated 
overtones  of  the  plate.  The  electrical  oscillation  persists  from  spark  to 
spark. 

This  explanation,  however,  encounters  difficulties  if  a  computation  of  the 
coefficient  L  is  made  from  the  known  R  and  C  values  at  the  crests.  Since  for 
the  coil  /,  R  =  3  2  ohms  and  L  —  0.2  henry,  and  for  the  telephones  in  parallel 
R  =  550  ohms,  2L  =  1.2  henries  (inductances  in  parallel),  the  logarithmic 
decrement  d  computed  as 

d  =  7T R/  V L/C -Ry 4 

comes  out : 

b&' crest,  C=o.ij  X  10-6  farads,  d=  0.80  0  =  2,934 

d’  crest,  C  =  o.035  10-6  d=  0.36  0  =  1,830 

Hence  if  L  is  computed  as  L  =  2/co2C(i  +  [d/ 4x)2),  since  the  telephones  are  in 
parallel, 

n—  467  -  bb'  crest  L  =  6.6hen. 

w=294  d' crest  3.4  hen. 

As  nothing  has  been  changed  in  the  secondary  but  the  pitch  n,  these 
values  ought  to  be  the  same,  which  is  far  from  being  the  case,  while  their 
magnitude  is  out  of  the  question.  It  is  obvious,  therefore,  that  either  some¬ 
thing  in  addition  to  the  mutual  induction  has  been  overlooked  or  that  the 
primary  harmonics  are  irrelevant.*  In  frequency  squared  d'/bb'  is  about  2.5, 
whereas  the  result  is  a  scant  2 .  There  is  nothing  else  but  these  two  pipe  notes 
(see  figs.  73  and  75)  to  which  the  two  maxima  can  be  referred,  unless  the 
sequence  adjustment  is  in  some  way  implicated. 

To  simplify  the  circuit  still  further,  the  telephone  T  was  cut  out  and  the 

*If  the  secondary  harmonics  be  taken  as  W  for  C  =  0.17  and  b b"  for  C  =  0.035,  the  L 
values  are  0.7  and  0.8  henry,  respectively,  the  actual  values  being  0.8  henry. 


PROBE  AND  THE  INTERFEROMETER  U-GAGE 


53 


data  of  figure  105  investigated.  The  curves  a  and  b  are  repetitions  made  at 
different  times,  the  break  pitch  being  d! .  The  crests  now  lie  at  C  values  about 
one-half  as  large  as  in  figure  104.  Nothing  has  been  done  but  a  removal  of 
the  telephone.  The  discrepancy  just  alluded  to  persists.  The  logarithmic 
decrements  being  d  —  0.41  at  W  and  smaller  are  not  of  immediate  consequence. 
The  L  value  for  the  W  crest  follows  from  C  below  0.02,  7^  =  1,110+32 
ohms,  which  gives  L  above  6.2  henries.  At  the  d'  crest,  C  is  above  0.075,  so 
that  L  is  below  4.0  henries.  The  results  are  thus  about  the  same  as  before  and 
out  of  all  proportion.  If,  however,  the  secondary  harmonics  are  \>b"  for  C  =  0.02 
and  W  for  C  —  0.075,  the  L  values  come  out  1.45  and  1.55,  respectively,  the 
actual  value  being  somewhat  above  1.4. 


39.  Detailed  survey  near  the  crest — If  we  bring  together  the  above  data 
for  the  C  position  of  the  flattish  crests  in  so  far  as  these  can  be  specified,  the 
results  may  be  tabulated  as  follows: 


Primary  pitch  W 


Primary  pitch  d' 


i+r  1 

(T+r 

C  =  0.07  mf. 

Fig.  102 

C=0.05  Fig.  98 

< 

\  V 

0.04 

103 

iT+r 

0.027 

100 

0.03  99 

1 

l  V 

0.015  and  0.055 

IOI 

h 

\r+r 

C  =  0.035  and  °-l7 

104 

V  1 

{ T 

0.02  and  0.08 

105 

T-\-Tf  denotes  that  both  telephones  are  used  together  in  parallel  circuits, 
but  vibrating  in  phase;  /+/',  that  the  two  secondaries  are  used  together 
in  series.  In  most  cases,  the  T'  values  of  C  are  about  one-half  the  T+T' 
values,  which  means  that  the  L  values  for  T-\-T'  are  half  those  for  T'  alone, 
since  LC  is  constant.  In  other  words,  the  inductances  are  in  parallel  in 
the  former  case. 

It  is  desirable,  however,  to  test  this  specifically  and  to  supply  the  missing 
brace  for  the  pitch  d'.  This  has  been  done  in  figures  106  to  112,  in  which  the 
inserts  (figs.  109  to  112)  show  how  T+T',  I+I'  are  to  be  understood.  The 
agreement  of  the  new  crests  with  the  old  is  satisfactory,  seeing  that  the  crests 
are  flat  from  the  large  resistances  in  circuit  and  considerable  lateral  shift  is 
therefore  inevitable.  The  new  and  old  graphs  may  be  regarded  as  coincident 
observations,  the  scale  of  the  fringe  deflections,  s,  being,  of  course,  arbitrary. 
If  we  compare  the  cases  T'  and  T+T'  at  the  same  pitch  (caet.  par.)  as  to  C 
positions  of  the  crests;  viz, 


Fig.  107  C= 0.04 
Fig.  106  C  =  o.oi4 
Fig.  hi  C  =  o.o6 
Fig.  109  C  =  o.oi5;  0.075 


Fig.  108  C=o.07 
Fig.  106  C  =  0.025 
Fig.  112  C  =  o.i2 
Fig.  no  C  =  0.035;  0.170 


the  C  of  the  latter  group  {T-\-T')  is  about  twice  the  former  (Tr),  meaning 
(since  LC  is  constant,  nearly)  that  L  is  halved  when  T-\-T'  are  in  parallel,  as 
it  should  be.  This  is  even  more  marked  for  the  double-crested  graphs  (figs. 
109,  no)  which  here  are  closely  tested.  Such  doublets  have  occurred  inci¬ 
dentally,  as  in  figure  101  (and  possibly  the  uncertain  arrangement  of  points  in 


54 


ACOUSTIC  EXPERIMENTS  WITH  THE  PIN-HOLE 


figures  107  and  108  might  be  so  interpreted,  the  two  C  positions  of  crests  in 
figure  107  being  about  doubled  in  figure  108,  nearly);  but  this  was  not  sus¬ 
tained.  The  relations  of  the  \>br  crests  and  the  d!  crests  is  far  from  obvious, 
as  one  would  surmise  that  n2LC  should  be  nearly  constant.  It  is  worth  while, 
therefore,  to  attempt  a  systematic  computation  of  the  various  cases  by  first 
finding  the  rough  value,  L=i/co2C;  from  this  L  to  compute  the  decrement  d 
and  then  a  corrected  L. 


* 

W 

I,T' 

7.  T  +  T 

1  + 1',  T' 

/+/',  T+T 

c= 

O.OI4 

O.O25 

O.04 

0.0  7 

L  = 

8-3 

9-3 

2.9 

3-3 

Fig. 

85 

85 

86 

87 

d' 

1+1',  T+T' 

I,  T 

I,  T  +  T' 

1  +  1',  T' 

0.015,  O.075 

0.035,0.170 

0.06 

0.12  m.f. 

7-8  3-9 

6.6  3.4 

4.9 

4.9  hen. 

88 

89 

90 

9i 

The  results,  even  granting  the  difficulty  of  placing  the  crests,  are  highly 
promiscuous  and  difficult  to  construe.  It  seems  certain  that  when  the  break 
corresponds  to  a  given  note,  W  or  d\  the  telephone-plate  vibrates  additionally 
with  an  overtone  that  happens  to  be  favored  by  the  pipe. 

To  indicate  the  apparent  irregularity  of  data,  the  ratios  of  computed 
L  values  for  an  I  and  I+If  adjustment  may  be  instanced.  Calling  this  ratio 
L/Z/,  the  results  are: 

/,  T'Qrb ') T'(d’)  ;L/Lf  =  8.3/ 3.9  =2.1 
I,  r+ r  ( w) r+  T\d)  8.3/34 = 2.7 

Mean  ratio,  2.4 


I+r,T'(\>b')  :I+r,T'(d')  :L/L’  =  2. 9/4.9  =  0.59 
/+/',  T+  T',  (W) :/+/',  T+  T'(d')  13.3/4.9  =  0.67 

Mean  ratio,  0.63 

* 


PROBE  AND  THE  INTERFEROMETER  U-GAGE 


55 


We  should  thus  have  to  increase  the  pitch  of  bfr',  V/2.4  =  1.55  times  in  the 

case  of  L,  V  (!>&'),  and  increase  the  pitch  of  d!  \A1.63  =  1.26  times  in  case  of 
L\  (I  +  I'),  (d')}  to  get  a  rough  coincidence  of  ratios.  This  would  imply  an 
active  harmonic  somewhat  above  /"in  the  first  and  a  #/' harmonic  in  the  second 
instance.  But  the  acoustic  tube  harbors  no  such  harmonics  in  the  phase 
adjustment  as  shown  in  figure  73.  They  do  occur  (nearly)  in  the  sequence 
adjustment  (figs.  73,  75),  which,  however,  is  certainly  ruled  out  in  all  combi¬ 
nations  T  +  T'.  Again,  not  only  is  the  passage  from  W  to  d'  accompanied  by 
opposite  effects  (rise  and  fall)  of  L  in  the  two  comparisons,  but  changes  of  L 
quite  of  the  same  character  take  place  in  passing  from  I  to  I  +  I'  at  the  same 
pitch.  Thus: 


Adjustment  b&' 

Adjustment  d' 

/,  V:  I+I',  T',  L/L' =  8. 3/2.9  =  2.9 
/,  T+T':  I+I',  7+r',L/L'=9.3/3.3=2.8 
Mean  ratio  2.8 

L/L’  =3.9/4.9=0.79 

L/L' =34/4.9  =  0.71 

Mean  ratio  0.75 

Here  the  effect  at  W  is  again  the  opposite  of  the  effect  at  d'  and  both  are  of 
the  same  order  as  in  the  preceding  case  involving  frequency  variation. 

Finally,  if  we  assume  the  L  of  the  coils  I  or  I'  to  be  the  same  (3.0  henry,  for 
example)  and  compute  the  frequency  from  the  capacities,  the  following  notes 
result : 


Break  at 

Break  at  d' 

/,  v  1,  r+r  i+r,  v  i+r,  t+t 
#/"  g"  W 

I,  Tf  I,  T+T'  /+/',  V  /+/',  T+T' 
f"U'  %e"d'  f  r 

in  which  we  merely  observe  a  promiscuous  group  of  high  notes  ( en  .  .  .  g") 
with  I  and  of  low  notes  (/'  to  a')  accompanying  (I  +  I').  Both  occur  at  the 
double  crests.  Nothing  has  been  gained  in  this  way. 


40.  Non-coupled  inductances  inserted.  Reductions — Owing  to  the 
difficulty  of  recognizing  the  particular  harmonic  to  be  selected,  it  seemed 
desirable  to  introduce  known  inductances  L  into  the  circuit,  to  facilitate  the 
recognition  of  the  actual  frequency.  The  scheme  is  shown  in  the  insert, 
figure  1 14.  The  inductances  L  =  o,  L  =  1,1  =  0.32  henry,  L  =  L3  =  1.4  henries, 
described  above  were  used.  It  was  found  that  the  greatest  care  had  to  be 
taken  with  the  tuning  to  discover  the  maximum  crest  among  the  crests  for  a 
small  off-tune.  If  that  is  not  done,  the  C  position  of  the  crest  will  be  too  low, 
as  it  undoubtedly  is  in  some  of  the  preceding  curves. 

Figure  113  presents  a  satisfactory  series  of  graphs  with  crests  at  (7  =  0.035 
for  L  =  o,  (7  =  0.025  for  L=Li,  and  C  —  0.015  for  L  =  L3.  If,  now,  we  compute 
the  total  self-induction  from  the  period,  without  regard  to  the  logarithmic 
decrement  (which  would  not  alter  the  case  appreciably,  because  of  the 
5 


56 


ACOUSTIC  EXPERIMENTS  WITH  THE  PIN-HOLE 


flatness  of  crests)  the  results  are  inadmissible  if  the  break-pitch  W  is  used; 
but  if  the  pitch  is  assumed  to  be  W\  the  first  overtone  of  the  break-pitch,  the 
results  are  reasonably  close  to  the  actual  values,  as,  for  instance: 


w2=  io6  X  8.61  X  4 

L t  +  T'  ==  hen. 

Lj  =  0.20  hen. 

Coil 

c= 

Total  L  = 

Do.  —I 

Actual  values 

0+1 r+r 
0.035 

0.83 

0 

0.60  +  0.20 

u+ i T+r 

0.025 

1. 16 

0.33 

0.32 

L3  +  I  T+T' 

0.015  mf. 

1 .94  henries 

1. 1 1  henries 

1.4  henries 

Thus  the  crest  for  curve  a  is  placed  fairly  as  to  the  C;  that  in  curve  b  is 
nearly  correct;  the  crest  in  curve  C is  apparently  too  high,*  but  the  correspond¬ 
ence  of  data  is  clearly  such  as  to  point  unmistakably  to  an  effective  pipe- 
note  Wf,  instead  of  b&',  the  pitch  of  the  break. 


r 


Further  tests  were  made  by  adding  (noninductively)  the  coils  Li  =  32 
henries  and  L3  =  1.4  henries  as  above.  The  crests  were  found  at  0.055  micro¬ 
farad  and  0.02  microfarad  respectively,  the  original  crest  (/')  being  at  0.18 
microfarad.  Hence 

Li=  (Ai/C)/co2  =  (18.2  —  5.6)79.63  =  1.31  hen. 

and 

L3  =  (50.0  —  5.6V9.63  =4.61  hen. 

if  the  pitch  of  the  secondary  is  b'.  But  as  these  results  are  four  times  too 
large,  the  pitch  must  have  been  b"  whence  Li  =  o.33  henry  and  L3  =  i.i5 

*It  is  more  probable  that  the  accepted  value  1.4  henries  for  this  coil  is  too  large. 


PROBE  AND  THE  INTERFEROMETER  U-GAGE 


57 


henries,  as  they  should  be.  This  promiscuous  octave  jump  of  pitch  is  very 
puzzling. 

In  view  of  this  reasonably  good  agreement,  it  is  worth  while  to  reexamine 
the- data  of  the  preceding  section,  as  it  is  already  probable  that  harmonics 
other  than  \>bf  and  W  do  not  occur,  even  when  the  break-pitch  is  d! .  The 
damping  coefficient,  moreover,  may  be  disregarded,  as  the  crests  are  too  flat 
for  precision.  Hence,  computing  L  from  the  observed  values  for  C  and  the 
appropriate  or(W ,  co2=  io6 X 8.61 ;  b&",  co2  =  io6X34.4),  the  following  adjust¬ 
ment  of  values  results : 


Circuit .  .  . 

I,  V 

I,  T+T' 

i+r,  t 

i+r,  t+t 

1,  T 

I,  T+T' 

i+rr 

i+r, 

T+T' 

Figure. . . . 
Break- 

106 

106 

107 

108 

109 

1 10 

hi 

1 12 

pitch .  . . 
Crest  at 

W 

W 

w 

w 

d* 

d' 

d' 

d' 

C  mf . . . . 
L  (henry) 
computed 

0.017 

0.025 

0.04 

0.07 

0.015  0.075 

0.035  0.17 

0.06 

O.I2 

from  C. . . 

1.71 

1. 16 

i-43 

1.04 

i-93  i*55 

0.83  0.69 

1.94 

0.97 

L  actual . . 
Pitch 

1.4 

.80 

i-55 

0.95 

1.4  1.4 

0.80  0.80 

1.6 

0.95 

taken . . . 

w 

w 

W 

w 

w  w 

]?b"  W 

W 

w 

In  case  of  figures  107,  108,  the  initial  C0  within  (/+/')  was  taken  as  0.03 
microfarad.  In  case  of  figures  m  and  112,  however,  the  curves  are  so  flat 
that  such  an  allowance  was  disregarded.  In  general,  though  the  coincidence 
is  very  rough,  the  values  of  L  computed  from  C  agree  with  the  actual  values 
as  closely  as  may  be  expected;  for  the  C  position  of  the  crests  admits  of  con¬ 
siderable  shifting. 

It  is  noticeable  that  the  d'  harmonic  does  not  occur,  except  at  the  break 
in  the  primary.  This  d'  merely  evokes  the  upper  harmonics  W  and  bb"  of 
the  phase  adjustment,  figure  73.  From  the  table  as  a  whole  there  can  be  little 
doubt,  I  think,  that  the  W  harmonic  does  actually  occur  acoustically  in  the 
tube.  Moreover,  the  double  crests  of  figures  109,  no  now  appear  as  octaves 
of  each  other,  which  is  a  much  more  plausible  interpretation  than,  the  sugges¬ 
tion  above.  This  is  also  true  of  the  phase  vibration  assumed  to  occur  in  all 
cases,  no  matter  whether  the  T  or  T  +  T'  adjustment  is  in  question. 

41.  Low-resistance  telephones — -In  the  preceding  experiments  the 
main  inductive  resistance  is  in  the  telephones  and  it  is  so  high  that  the 
required  crest  capacity  must  be  correspondingly  low.  Hence,  by  diminishing 
the  L  of  the  telephones,  a  larger  number  of  steps  in  C  are  at  once  available 
without  reducing  the  smallest  capacity  below  0.0 1  microfarad.  Naturally, 
the  method  is  restricted  to  smaller  values  of  the  L  examined. 

Figure  114  gives  the  results,  the  graphs  (I,  T+T',  and  I,  T')  corresponding 
to  figure  106.  The  method  is,  within  its  range,  much  more  sensitive  (3  cells 
and  100  ohms  in  circuit).  Owing  to  the  change  of  telephones  (new  pipe  tt, 


58 


ACOUSTIC  EXPERIMENTS  WITH  THE  PIN-HOLE 


figure  88,  and  new  pin-hole  probes)  the  fundamental  is  now  b'{ co2=  io6X9.63), 
in  addition  to  which  6"(w2  =  4X  io6X9.63)  often  appears.  The  low  crest  is 
now  at  /'. 

In  the  graphs  a  and  b  the  steps  are  o.i  microfarad.  There  is  no  minimum, 
At  C  =  oo  (short  circuit)  the  fringe  displacement,  s,  reaches  a  low  asymptote. 
Within  the  first  o.i  microfarad,  observations  are  made  in  steps  of  o.oi  micro¬ 
farad,  with  the  object  of  locating  an  anterior  crest;  but  none  could  be  found. 
In  the  graphs  d,  e,  the  interval  C  =  o.i  to  0.2  is  explored  in  steps  of  0.01 
microfarad,  to  locate  the  maxima  more  nearly. 

In  the  case  of  graph  c ,  the  pitch  of  the  primary  circuit  was  /'.  Here  the 
region  between  C  =  o.i  and  0.2  was  also  explored  in  steps  of  0.0 1  (not  shown) 
to  locate  the  maximum,  at  a  somewhat  different  intensity.  But  one  crest  was 
found  and  not  two,  as  in  the  corresponding  figure  no.  All  these  crests  are 
at  b'  pitch  in  the  secondary. 

Inserting  an  additional  noncoupled  inductance  1,1  =  0.32  henry  in  graph  / 
and  L3  =  i.4  henries  in  graph  g,  however,  the  crest  in  both  cases  appears  at 
b"  in  the  secondary,  the  primary  and  telephone-pitch  remaining  at  6',  sharply. 
These  graphs  indicate  the  rapid  dwindling  of  fringe  displacement,  s,  with 
increasing  L.  Here  also  but  one  crest  appears,  the  search  for  b'  being  unsuc¬ 
cessful.  The  great  difficulty  in  this  work  throughout  is  the  sharpness  of  the 
tuning  necessary,  which  must  therefore  be  repeated  at  each  observation.  A 
fraction  of  a  semitone  produces  a  large  5-effect  and  hence  the  graphs  a  ....  / 
can  not  be  obtained  quite  smoothly,  nor  the  maximum  selected  with  precision. 

The  puzzling  feature  here  again  encountered  is  the  apparently  arbitrary 
selection  of  the  harmonics  b '  and  b" ,  under  virtually  identical  pitch  of  the 
primary.  Sometimes,  as  in  the  above  graphs,  both  appear.  It  is  possible 
that  the  sufficient  nearness  of  the  step  in  C  to  the  particular  C  for  a  maximum 
determines  the  subtle  conditions.  Chladni  plates,  moreover,  behave  not 
unlike  this;  but  in  the  present  experiments  the  irregular  behavior  is  consistent. 

It  is  finally  necessary  to  give  the  data  corresponding  to  the  maxima 
inferred  from  the  curves,  remembering  that  this  can  not  be  done  with  pre¬ 
cision,  because  of  flatness  and  tuning  difficulties. 


Pitch  of  primary . . . 

6' 

6' 

6' 

6' 

r 

0,2  =  106X9.63 

Figure  1 14,  graph . . 

ad 

be 

/ 

g 

c 

Pitch  of  secondary . 

6' 

6' 

6" 

6" 

6' 

Circuit . 

i,  r+r 

/,  T 

Li+/,  r+r 

U+I,  T+T' 

I,  T+T' 

Crest  at  C . 

0.19 

0.17 

0.055 

0.02 

0.17 

mf. 

Total  L . 

0.56(6') 

0.61  (6') 

1.89 

0.61 

hen. 

Individual  L . 

0.14(6") 

0.15(6") 

0.33 

UI5 

0.15 

hen. 

Actual  L . 

0.18 

0.21 

0.32 

1.4 

0.18 

hen. 

In  the  cases  ad  and  be  the  L  refers  to  the  whole  circuit  secondary  and 
telephones,  the  actual  L  to  the  summarized  coefficients  of  self-induction;  so 
that  the  b '  pitch  assumed  for  curves  a,  d ,  b,  e,  c,  must  also  be  estimated  as  b", 


PROBE  AND  THE  INTERFEROMETER  U-GAGE 


59 


though  both  fit  badly.  In  case  of  the  graphs  /  and  g  the  coefficients  for  Li 
and  L3  are  found  from 

L  =  —  (i/Cl  +  7-i/C7)=(Ai/C)/«2 
or 

The  differences  are  within  the  possible  shift  of  the  eye-location  of  the  crest. 

42.  Spring  mercury  contact-breaker  of  inaudibly  low  pitch — As  in  the 

above  experiments  with  low  pitch,  the  primary  d!  and  /'  did  not  appear  in 
the  frequencies  of  the  secondary;  and  as  the  acoustic  pipe  is  often  multireso¬ 
nant  for  low  frequencies,  the  spring  contact-breaker  of  fixed  pitch  suggests 
itself  for  trial.  This  completely  replaces  the  electric  siren  or  contact-breaker 
of  variable  pitch;  but  naturally  calls  for  more  current  (3  cells  and  5  ohms  were 


used  in  the  primary) .  The  mercury  contact-breaker  must  be  neatly  made  with 
provision  for  washing  the  surface  (heretofore  described).  Its  performance  is 
then  surprisingly  steady,  as  shown  by  the  graph,  figure  1 15.  The  fringes  take 
a  definite  position  almost  at  once  and  no  tuning  difficulties  are  involved. 
Eventually,  however,  the  fringe  position  becomes  more  and  more  fluctuating 
and  frequent  cleaning  is  thus  necessary.  In  the  lapse  of  time,  moreover,  the 
^-values,  as  a  whole,  may  increase  or  fall  off,  so  that  the  graph  should  be 
covered  twice  in  opposite  directions. 

Two  springs,  a  lighter  (L.  S.)  and  a  heavier  one  ( H .  5.),  the  taps  of  each  of 
which  could  just  be  distinguished  by  the  ear,  were  first  used,  both  with  the 
single  (7,  T')  and  double  telephone  {I  T-\-  T')  adjustment.  The  data  are  given 
in  full  in  figures  115  and  116,  both  in  steps  of  0.1  microfarad  and o. 01  microfarad 
as  indicated.  The  tendency  to  flatness  at  the  crests  is  often  annoyingly 
present.  Even  when  crests  are  reached  rapidly  the  descent  of  curves  there- 


60 


ACOUSTIC  EXPERIMENTS  WITH  THE  PIN-HOLE 


after  is  relatively  slow.  They  all  pass  through  minima,  the  run  being  observed 
as  far  as  2 .2  microfarads  and  the  eventual  high  value  of  the  asymptote  for  C  =  °° 
(short  circuit).  The  graph  at  C=  00  is  in  fact  usually  above  the  crest-level  in  s. 
The  data  found  are  as  follows  (L.  S.,  light  spring;  H.  5.,  heavy  spring) : 


Primary  break. . 

L.  S. 

H.  S. 

L.  S. 

Figure . 

115a 

115c 

1 1 6a 

Pitch  of  sec . 

b" 

b" 

b" 

Circuit . 

i,  r 

I,  V 

IT 

Crest  at  C . 

0.13 

0.14 

0.14 

Total  L . 

0.20I 

0.19 

0.18 

Actual  L . 

0.26 

0.26 

0.21 

H.  S. 

L.  S. 

H.S . 

1 16  d 

1 16  b 

n6e 

b" 

b" 

b" 

IT 

r,  T+r 

T  +  r 

0.15 

0.18 

0.18 

m.f. 

0.17 

0.16 

0.16 

hen. 

0.21 

0.18 

0.18 

The  results  show  that  when  but  one  telephone  is  in  circuit,  the  C  value  of 
the  crest  which  appears  may  be  wavering.  The  pitch  b"  had  to  be  taken 


throughout,  whereas  the  pipe-note  is  b'.  When  both  telephones  are  used  in 
phase,  however,  the  position  of  the  crest  is  normal,  so  far  as  it  can  be  specified. 
This  adjustment,  together  with  the  lighter  or  faster  spring  (compare  curves 
a,  a",  b'}  b,  with  c,  c'  for  the  heavier  spring  in  figures  115  and  116),  is  also  far 
more  sensitive  and  should  therefore  be  preferred. 

43.  Inductor  with  variable  core — As  the  spring  contact-breaker  requires 
relatively  large  currents  to  keep  it  going,  the  primary  and  secondary  currents 
are  excessive.  To  cut  the  secondary  down  by  a  resistance,  as  in  figure  117, 
curve  c  (3  cells  and  2  ohms  in  primary)  where  2,000  ohms  are  inserted,  obliter¬ 
ates  the  crest  altogether.  To  obviate  large  resistances  in  the  secondary,  the 
usual  device  of  a  weaker  or  a  sliding  primary  is  available.  Curves  a,  a'  show 


PROBE  AND  THE  INTERFEROMETER  U-GAGE 


61 


the  results  when  the  coil  L\  was  used  as  a  secondary  accompanied  by  a  suitably 
weak  primary  (3  cells  and  5  ohms),  here  quite  within  the  former.  The  lighter 
mercury  spring-break  functioned  faultlessly.  The  crest  is  sharply  determin¬ 
able  and  the  rapidly  falling  curves  pass  through  a  flat  minimum.  Assuming 
that  the  effective  harmonic  is  and  C  =  0.08 

L  =  i/(4  X  9-63  X  0.08)  =  0.325  henry, 

the  estimated  value  for  the  circuit  being  (0.32+0.03)  or  0.35  henry. 

Using  3  cells  and  3  ohms  in  the  primary,  the  graphs  were  considerably 
sharpened,  as  shown  in  curves  b  and  b',  figure  117.  The  crest  may  here  be 
placed  at  0.075,  so  that  the  accuracy  should  approach  1  per  cent.  The  result 
is  L  =  1/(4X9-63X0.075)  =0.337  henry. 


A  spring  interrupter  of  the  usual  hammer  type  with  platinum  contacts 
was  next  tried.  Its  note  was  audible  and  placed  by  the  ear  at  a  frequency  of 
about  n  —  100  per  second.  The  results  are  given  in  figure  118a,  where  it  was 
necessary  because  of  the  large  n  and  therefore  intense  secondary  currents,  to 
withdraw  about  half  the  core  out  of  the  inductor  L\.  The  curve  here  is  quite 
different  from  figure  117.  The  crest  is  not  symmetrical  and  the  flat  but 
relatively  high  minimum  finally  ascends  to  an  enormously  high  asymptote, 
5  =  120,  for  C=  00  (short  circuit).  Estimating  the  crest  as  placed  at  £7  =  0.1 6 
microfarad, 

L  =  i/(4  X  9.63  X  0.16)  =0.162  henry 

(if  the  note  is  bb"),  which  is  somewhat  less  than  half  the  value  for  the  pre¬ 
ceding  full  circuit,  as  it  should  be.  Such  an  apparatus  is  extremely  convenient, 
if  the  nonsymmetrical  graph  (possibly  associated  with  the  brush  on  sparking) 


62 


ACOUSTIC  EXPERIMENTS  WITH  THE  PIN-HOLE 


can  be  modified.  Using  the  full  core  and  2,000  ohms  in  the  secondary,  the 
curve  b  without  a  definite  crest  and  corresponding  to  the  curve  C  in  figure  1 1 7 
was  obtained.  If  the  crest  is  placed  at  £  =  0.3  microfarad,  the  maximum 
elevation,  L  =  0.35  henry,  which  is  again  a  correct  order  of  value. 

A  number  of  incidental  experiments  were  made  with  the  inductors  I,  I' 
(now  used  as  test  objects),  while  Li  supplies  the  induced  current.  Figure  119 
is  a  summary  of  results  with  the  lighter  mercury-break,  the  coil  combinations 
being  indicated  on  the  curve.  The  maxima  selected  are  also  shown.  If 
co2  =  4X9.63  Xio6  ( "),  the  results  are 

LhT+T'  C  =  o.o8mf.  -£1=0.33  hen. 

Li+I,  T+T'  0.05  7=0.19 

T/i+7',  T+T'  0.055  7' =0.15 

smaller  steps  in  C  would  have  been  desirable. 


The  same  experiment  performed  with  the  platinum  spring-interrupter  and 
the  approximately  half-coil  %L\  (coil  half  withdrawn),  figure  120,  gave  in  the 
same  way 

xLi,  T+T'  C  =  o.i8mf.  *7,1=0.14 
*7,1+7,  T+T'  0.075  7  =  0.20 

xLi+T,  T+T'  0.085  I'  =  0.1 6 

The  crests  in  both  groups  of  experiments  are  unfortunately  very  flat. 

44.  Increased  currents — The  surprisingly  good  performance  of  the 
platinum  spring-interrupter  induced  me  to  test  it  further  by  increasing  the 
current ;  for  it  is  clear  that  the  sharpness  of  the  crest  must  increase,  as  the 
currents  are  continually  larger.  The  limits  to  this  method  are  given  by  the 
insulation  of  the  condenser,  which  would  eventually  be  sparked  through  and 
should  therefore  be  specially  constructed.  Nevertheless,  the  graphs  of  figure 
1 2 1,  obtained  with  the  inductance  L3=  1.4  (roughly),  indicate  the  availability 


PROBE  AND  THE  INTERFEROMETER  U-GAGE 


63 


of  the  method.  The  curve  b  for  weak  currents  is  at  once  improved  in  the 
curves  a  or  a'  for  stronger  currents,  in  relation  to  sharpness  of  peaks.  It  is 
also  obvious  that  continuous  change  of  C  between  the  steps  would  ultimately 
be  necessary.  The  usual  disk  type  is  not  satisfactory  for  this  purpose,  as 
sparks  soon  break  across  the  air-gaps. 

With  the  crests  at  C  =  0.02  microfarad,  L  —  1/9.63X0.02  =  1.3  henries, 
the  only  demand  being  smaller  stops  near  the  crest.  Withdrawing  the  core 
partially  reduced  L  to  0.15  henry.  The  note  was  b". 

The  graphs  figure  122,  a,  a',  show  the  results  when  the  core  is  drawn  out 
about  one-half  and  b  when  drawn  out  about  three-quarters.  With  the  crests 
placed  at  C  —  0.047  and  °-°8  microfarad,  the  values  are  L  =  0.55  and  0.32 
henry  respectively,  the  note  being  again  b" .  The  necessarily  flat  crest  of  the 
graph  b  could  have  been  sharpened  by  increasing  the  current  in  the  primary. 


Attempts  made  very  cautiously  (fig.  123)  with  a  larger  coil,  and  very  weak 
currents  gave  a  sprawling  graph  with  crests  at  C  =  o.oi  and  0.04.  These  are 
probably  the  notes  bf  and  b"  and  give  L  =  2.6  and  2.7  henries,  respectively. 

46.  Longer  and  wider  organ-pipe — This  was  provided  with  the  object  of 
getting  a  lower  fundamental,  the  pipe  being  of  inch  brass  tubing  and  24.1  cm. 
long  between  telephones.  A  survey  of  the  harmonics  made  with  the  motor- 
break  (3  cells,  100  to  200  ohms,  telephones  in  parallel,  and  without  other 
induction  coils)  is  reproduced  in  the  graphs,  figure  124,  with  extremely  sharp 
crests,  so  that  only  approximate  pitch  location  was  possible;  i.  e.,  intervals 
within  a  fraction  of  a  semitone  produced  enormous  fringe  displacement 
differences.  Probably,  from  the  width  of  the  tube,  there  was  no  reaction 
below  /'  (traced  to  c ) .  The  multiresonance  of  thinner  tubes  in  this  region  is 
thus  absent.  At  W  and  \>b"  occur  sharp  cusps,  with  the  fringes  projected  out 


64 


ACOUSTIC  EXPERIMENTS  WITH  THE  PIN-HOLE 


of  the  field  of  view.  If  these  are  (phase  adjustment)  the  first  and  second 
overtones  of  the  pipe  for  a  fundamental  at  b&,  it  is  as  usual  difficult  to  account 
for  the  /'  (which  is  quite  strong)  unless  it  also  evokes  /".  The  electric  oscilla¬ 
tion  (see  below)  contributed  a  marked  which  could  not  be  reached  by  the 
motor-break. 

In  the  sequence  survey,  only  a  faint  d"  (5  =  20)  could  be  detected. 

The  new  pipe,  producing  almost  the  same  notes  as  the  thin,  narrow  pipe, 
is  disappointing.  The  oscillation  phenomenon,  from  the  larger  body  of  air 
to  be  kept  in  motion  by  the  telephones,  was  bound  to  be  weaker.  Little  was, 
therefore,  done  with  the  tube  in  this  place,  beyond  the  tests  shown  in  the 
graphs,  figure  125,  with  the  circuit  as  shown  in  the  insert  and  a  platinum 
break  in  the  primary  (3  cells,  5  ohms).  The  small  induction  coil  furnished  its 
own  appurtenances,  the  core  being  quite  in. 

In  one  respect  the  data  of  curve  a  are  novel,  for  the  harmonics  marked 
on  the  graph  could  be  distinctly  heard  in  the  telephone.  If  one  computes  the 
frequencies  n  which  for  L3=  1.4  should  belong  to  the  chosen  capacities,  the 
series  is 


C  =  o.oi 

0.02 

0.03 

0.04 

0.05  mf. 

n  =  I>35° 

955 

0 

00 

!>. 

67O 

600 

/"' 

b b"-b" 

g" 

e"-f" 

#d" 

Heard,  #  f'" 

b  b" 

g" 

e" 

id”) 

which  is  an  attempt  at  coincidence  and  might  be  improved  with  a  larger  L 
value.  It  seems  clear  that  the  frequencies  of  electric  and  acoustic  oscillations 
near  f"  were  close  enough  to  excite  the  high  harmonic,  and  this  accounts  for 
the  distorted  curve  a  in  figure  125.  The  b6",  moreover,  is  the  octave  above 
the  survey  cusp  in  figure  124.  None  of  the  other  crests  were  sufficiently 
approached  by  the  C  values  to  be  stimulated. 

Repeating  this  experiment  with  a  modified  break,  only  the  W  harmonic 
could  be  heard  and  the  graph  took  the  normal  form  of  curve  b  in  figure  125. 
These  experiments  indicate  the  difficulties  encountered  with  the  platinum 
spring-break,  inasmuch  as  it  is  liable  to  change  its  pitch  capriciously,  accen¬ 
tuate  successive  harmonics  of  the  organ-pipe,  and  lead  to  distorted  graphs. 
The  curve  a,  for  instance,  should  probably  be  indented  in  the  way  suggested 
in  figure  125.  The  motor-break  is  relatively  free  from  such  annoyances. 

46.  Long,  thin  pipe — Relatively  large  currents  are  needed  to  energize  the 
preceding  wide  pipe,  and  this  sometimes  makes  the  spring-break  rattle  and 
function  irregularly.  The  long,  thin  pipe  (23.7  cm.  long,  scant  1  cm.  in  diam¬ 
eter)  is  not  only  much  more  sensitive  in  relation  to  the  pin-holes,  but  responds 
to  a  nearly  quiet  spring-break  and  the  fringe  displacements  are  usually  remark¬ 
ably  constant.  The  results  are  summarized  (fig.  126)  in  the  curves  a  and  6. 
The  curve  c  is  a  later  repetition  at  the  curious  bump  between  C  —  0.3  and  0.5 
microfarad,  showing  it  to  be  real.  After  passing  <7  =  0.3  microfarad,  the  break 
in  the  primary  begins  to  be  more  and  more  noisy.  This  indicates,  I  think, 


PROBE  AND  THE  INTERFEROMETER  U-GAGE 


65 


that  the  primary  crest  is  actually  being  approached,  as  C=  <»  shows  less 
fringe  displacement.  If  the  effective  frequency  were  still  a"  and  the  crest 
were  to  be  located  at  i  microfarad,  L  =  o.o3  microfarad  would  be  the  coefficient 
of  the  primary.  The  crest  is  certainly  higher  and  the  coefficient  smaller. 

To  interpret  figure  126,  it  is  necessary  to  make  the  survey  in  pitch  given 
in  figure  127,  the  circuit  being  without  inductances  other  than  those  in  the 
telephones.  The  tube  harmonics  are  thus  a'  and  a"  (in  the  phase  adjustment; 
the  sequence  note  should  thus  be  at  a).  The  lower  a  of  the  graph  probably 
evokes  one  of  these  upper  notes.  One  would  expect  an  intermediate  e",  but 
the  pipe  gives  f"  and  below  (between  a  and  a')  is  a  d'  not  easily  accounted  for, 
although  quite  strong.  If  a"  is  effective,  co  =  io3X5-53  and  co2  =  io7X3.o6, 


the  datum  already  used.  Placing  the  crest  in  figure  126,  curve  a  at  (7  =  0.025, 
the  inductance  would  be  L3  =  1/30.6X0.025  =  1.3 1  in  as  good  agreement 
with  the  earlier  results  as  may  be  expected.  The  notes  heard  in  the  telephone 
are  marked  on  curve  a,  figure  126,  and  also  inserted  in  figure  127.  They  vary 
somewhat  with  the  adjustment  of  the  break;  but  the  high  notes  e'"  and  g"  are 
pretty  clear  and  fixed.  It  is  interesting  to  find  the  frequency  at  the  bump 
of  curves  a  and  c,  postulating  C  =  0.06  here.  It  is  d",  and  for  this  there  is  no 
warrant  in  figure  127.  Some  other  reason  must  therefore  be  sought  for  it. 
So  also  the  notes  heard  in  the  telephone,  as  indicated  in  figure  127,  have  no 
definite  relation  (excepting  the  /")  to  the  pipe  harmonics.  Possibly  d\  d ", 
/",  #g",  e,n  may  be  plate  harmonics.  Alternatively,  one  may  suspect  the 
occurrence  of  forced  vibrations,  with  the  spring-break  dominant.  The 
impotence  of  the  long,  wide  pipe  in  §  45,  for  instance,  is  evidence  in  point. 


66 


ACOUSTIC  EXPERIMENTS  WITH  THE  PIN-HOLE 


47.  Short,  thin  pipe — With  the  present  pipe  (cut  down  to  length  io  cm., 
diameter  i  cm.)  no  greater  sensitiveness  need  be  expected;  but  the  obtrusive 
harmonics  would  be  diminished,  it  was  thought.  This  is  hardly  the  case  in 
the  survey  in  pitch,  summarized  in  the  lower  curve  a  of  figure  128.  Crests 
occur  at  about  half  a  semitone  below  d',  g',  d",  g",  and  an  intense  one  (found 
by  the  electric  oscillation)  at  d'".  The  crest  at  g"  is  for  some  reason  (break 
irregularity)  very  small,  though  none  the  less  definite.  One  may  as  usual 
suppose  that  pipe  and  plate  harmonics  are  superposed.  No  crests  were  found 
below  d'. 

If  we  consider  g  the  fundamental,  the  odd  and  the  even  harmonics  would 
all  be  present  (except  the  first)  in  the  phase  adjustment.  This  is  quite  unex¬ 


pected,  unless  there  is  secondary  stimulation.  The  telephone  resistance  was 
600  ohms. 

When  tested  by  the  small  inductor  L3  with  platinum  break  (3  cells  with 
resistance  in  the  primary;  about  1,000  ohms  in  the  secondary),  the  graphs  b 
(steps  0.1  microfarad)  and  b'  (steps  0.0 1  microfarad)  were  obtained.  The 
crest  may  be  located  at  C  =  0.015  microfarad.  Putting  go  =  io3X3.54  for  the 
slightly  flatted  d"f  since  co2  =  io7X  1.256,  L3  =  5.29  henries.  This  is  about 
four  times  too  large,  so  that  if  co2  =  io7X5-02,  L3=  1.32  henries,  the  correct 
order  of  value.  Hence  the  dominant  note  must  have  been  d"'  as  indicated 
by  the  cusps  in  figure  128,  curve  a.  In  curve  b,  beyond  the  minimum,  the 
spring-break  begins  to  rattle  sonorously.  The  curve  then  rises,  finally  to  fall 
again  into  5  =  50  for  C—  0° .  It  seems  probable  that  the  spring-break  and  the 
electric  oscillation  are  approaching  resonance. 

The  primary  of  L3  was  now  provided  with  a  new  weak  secondary  LA  of 


PROBE  AND  THE  INTERFEROMETER  U-GAGE 


67 


about  150  turns  of  wire.  On  being  tested,  it  gave  the  results  reproduced  in 
curve  c,  figure  129.  The  crest  here  is  apparently  near  C  —  o.g  microfarad,  but 
may  be  beyond  the  figure.  If  the  note  is  d"\  L  —  0.022  microfarad,  or  some¬ 
what  smaller. 

To  this  secondary  LA  the  coil  L\,  with  the  core  removed,  was  now  added. 
The  effect  is  shown  in  figure  129,  curve  d.  With  the  crest  placed  at  C  —  0.45 
microfarad  and  the  same  note  d"\  the  new  coefficient  would  be  LA  +  Li  =  0.044 
henry,  giving  0.022  henry  for  the  coil  Li  alone.  On  thrusting  the  core  into 
Li,  the  current  was  almost  entirely  cut  off;  but  a  crest  at  C  =  o.o6  to  0.07 
could  just  be  detected.  If  the  note  is  again  d'",  this  makes  Li  =  o.3  about, 
which  is  correct  in  order  of  value. 

It  would  not  have  been  difficult  to  increase  the  currents  in  the  secondary 
by  the  corresponding  increase  in  the  primary;  but  because  of  the  danger  of 
sparking  through  the  condenser,  this  was  not  attempted. 

As  the  crest  of  the  core  LA  is  not  quite  within  reach,  another  similar  coil, 
Lb,  was  wound  with  somewhat  thinner  wire.  The  graph  is  given  in  figure 
1290,  where  the  crest  is  definitely  between  C  =  0.8  and  0.9  mf.  If  £  =  0.85  is 
taken,  L  =  0.0234  henry.  In  their  initial  progress  the  curves  c ,  d,  e  run  very 
closely  together. 

In  case  of  the  graphs,  figure  130,  L  =  0.010,  0.020,  0.030  henry,  respectively, 
were  added  to  the  secondary  circuit,  Lb-  Taking  £*  =  0.57,  0.45,  0.35  for  the 
crests,  since  a>2  =  io7XS-o2,  L  =  o.on,  0.021,  0.033  henry  if  Lb  =  0.023  henry, 
which  is  good  corroboration  for  all  the  inferences  involved. 

48.  Long  and  short  pipes  compared.  Combined  primaries — The  fre¬ 
quent  occurrence  of  crests  which  have  no  equivalent  in  the  electric  oscillations, 
silent  crests  as  it  were,  induced  me  to  prepare  a  very  long  (length  30  cm., 
diameter  scant  1  cm.)  thin  pipe,  which  would  naturally  be  expected  to  harbor 
many  nodes  of  high  pitch.  The  acoustic  survey  of  this  pipe  so  far  as  attained 
is  shown  in  figure  13 1,  which  was  difficult  to  construct  by  ear  methods,  because 
of  the  sharpness  and  proximity  of  the  cusps.  The  maxima  e',  g',  a',  e ",  g" 
stand  forth  very  well ;  but  below  c'  there  is  liable  to  be  too  much  intricacy  to 
be  fully  made  out.  Between  e"  and  g"  one  is  often  at  a  loss,  and  it  was  imprac¬ 
ticable  to  go  higher. 

In  figure  132a,  the  case  of  LB,  alone,  is  worked  out,  capacities  (see  insert) 
varying  in  steps  of  0.1  microfarad.  There  is  no  real  crest,  but  rather  a  flat 
plateau  to  the  curve,  after  C  =  o.8  microfarad  is  passed;  but  the  low  C=  °° 
proves  that  a  marked  crest  must  occur.  If  we  take  C  =  o.8  microfarad  as  the 
maximum,  the  note  for  LB  =  0.023  will  again  have  to  be  d"\  as  in  figure  128. 
This  is  out  of  immediate  correspondence  with  figure  1 3 1 ,  except  in  relation  to 
g'  and  g";  but  it  is  otherwise  not  unexpected  in  relation  to  g',  since  the  pipe 
is  just  three  times  as  long  as  the  short  pipe.  As  usual,  the  notes  vary  slowly 
in  pitch  on  the  plateau,  but  relatively  fast  nearer  the  anterior  parts  of  the 
graph.  The  probability  of  e'",  g"',  a'"  cusps  is  without  evidence  in  figure 
132a,  and  there  is  no  indication  that  a  continuous  C  change  would  have 


68 


ACOUSTIC  EXPERIMENTS  WITH  THE  PIN-HOLE 


introduced  other  cusps.  The  distribution  of  notes  in  the  earlier  curve  may 
therefore  be  reproduced  here. 

Owing  to  the  remoteness  of  the  crests  in  curve  a  ( LB ,  telephones  only), 
the  additional  inductance  of  coefficient  L\  (0.32  henry)  was  inserted.  The 
latter  was  provided  with  a  primary  (without  break)  joined  in  series  with  the 
primary  of  LB  (see  insert).  The  resistances  being  low,  the  simple  platinum 
break-hammer  of  LB  functioned  satisfactorily.  For  convenience,  the  second¬ 
aries  were  also  joined  in  series,  making  a  total  coefficient  L  =  o. 32  +  0. 02  =  0.34 
henry. 

The  graph  1326  was  obtained  with  the  long  pipe  (length  30  cm.,  diam¬ 
eter  1  cm.)  in  this  way.  The  curve  is  interesting,  as  it  actually  exhibits  two 
crests.  If  the  first  is  located  at  <7  =  0.15  microfarad  and  the  note  is  below 
e"(co2  =  4X4.46Xio6),  L  =  0.37  henry,  in  excess  of  the  actual  value  stated. 


•  If  the  crest  is  located  at  <7  =  0.14  microfarad  and  the  note  is  g"(co2  =  4X5.91  X 
io6),  L  =  0.30  henry  below  the  actual  value.  The  crest  found  in  the  graph, 
<7  =  0.15,  may  therefore,  in  correspondence  with  the  e"y  g”  vagueness  of  figure 
13 1,  be  regarded  as  a  superposition  of  the  two.  Again,  if  the  second  crest  is 
placed  at  <7  =  0.5  microfarad  and  the  note  is  g'(co2  —  io6X5-9i),  L  —  0.34  at 
once  in  fair  agreement  with  the  actual  value,  even  if  the  crest  is  flatter.  On 
the  other  hand,  e',  a',  a",  gave  no  interpretable  electric  equivalent,  the  pitch 
a  being  left  out  entirely  in  figure  132 b,  as  the  annotations  “crest”  indicate. 
Again  one  suspects  the  dominance  of  the  spring-break. 

The  same  adjustment  was  now  made  for  the  short  pipe  (length  10  cm., 
diameter  1  cm.)  with  results  recorded  by  the  figure  132,  graph  c.  There  is 
here  but  one  crest,  near  <7  =  0.06  microfarad.  If  the  note  (according  to  fig. 
128a)  is  near  d'"(u2  =  io6X 50.2),  L  =  0.33  henry,  a  little  short  of  the  actual 
value,  showing  that  the  rounded  <7  =  0.06  microfarad  is  not  the  peak  of  the 
crest. 

From  the  total  coefficient  L  —  (0.32+0.02)  =0.34  henry,  I  now  computed 


PROBE  AND  THE  INTERFEROMETER  U-GAGE 


69 


the  frequencies  corresponding  to  each  of  the  steps  C  —  o.  i,  in  the  curves  b  and  c. 
For  C  —  o.i,  0.2,  etc.,  the  nearest  note  has  been  inscribed  in  the  curves. 
Particularly  in  case  of  graph  c,  it  is  noteworthy  that  the  crests  found  in  the 
graph  figure  128a,  with  the  possible  exception  of  d\  make  no  impression  on 
the  former,  as  the  attached  legends,  “crests,”  indicate.  Thus,  for  instance, 
the  g'  crest  in  figure  128a  actually  coincides  with  the  minimum  at  C  =  o.5 
in  figure  132c,  where  the  note  is  g'.  The  same  has  been  indicated  in  figure 
129c,  in  figure  132c,  and  elsewhere.  Curiously  enough,  in  curves  b ,  c  of 
figure  132,  the  acoustic  g'  crest  lies  respectively  at  a  crest  and  at  a  trough. 
Hence  also  the  reasonable  surmise  that  the  troughs  of  the  acoustic  graphs 
(pitch)  ought  to  coincide  with  the  troughs  of  the  electric  graphs,  receives  no 
warrant  from  the  experiments.  It  has  been  suggested  that  if  the  passage  in 
C  from  step  to  step  were  made  continuously,  the  missing  crests  might  appear; 
but  in  a  number  of  cases  in  which  this  was  tried,  the  crests  in  question  remained 
absent,  unless  they  were  foreshadowed  by  the  steps  and  merely  intensified  by 
continuous  changes  of  C.  Hence,  since  the  survey  is  made  by  a  direct  current 
interrupted  by  the  periodic  break  without  appreciable  electric  oscillation 
(i.  e.,  no  condenser,  see  fig.  124),  whereas  in  case  of  the  platinum  spring-break 
of  fixed  pitch,  the  presence  of  a  condenser  determines  the  oscillation  (both 
acoustic  and  electrical),  the  missing  crests  must  be  in  some  way  associated 
with  this  difference  of  excitation.  The  direct  current,  periodically  interrupted, 
is  under  better  conditions  to  force  a  vibration  than  is  the  self-starting  electric 
oscillation.  Practically  this  is  an  advantage,  since  an  abundance  of  harmonics 
would  be  bewildering.  If  C0  is  the  step  unit,  so  that  C  =  ncCo,  and  if  AT  is  the 
frequency  of  the  nth  harmonic  found,  N  =  nhNo  (even  harmonics  in  the  phase 
adjustment,  No  being  the  fundamental  frequency) 

nh2nc  =  1  / (i67tWo2LC0)  constant, 

so  that  a  series  nAnc  —  n\zn'c,  etc.,  is  implied,  each  pair  nAnc  corresponding 
to  a  crest.  But  as  a  rule  only  one  pair  is  found. 

In  other  respects,  the  remarks  already  made  relative  to  high  and  low 
C  values  apply.  The  purpose  of  using  the  electric  oscillations  to  interpret  the 
amazing  presence  of  very  low  notes  associated  with  very  short,  slender  pipes 
has  thus  in  a  measure  succeeded. 

49.  Opposed  mutual  inductions  and  similar  comparisons — In  figure  133 
I  have  recorded  another  set  of  experiments,  in  which  two  coils  in  series  Li 
and  Lb  in  the  secondary,  or  I  and  I',  were  actuated  by  their  primaries,  also  in 
series,  in  the  same  or  in  opposed  directions.  Hence  the  sum  or  the  difference  of 
induced  electromotive  forces  is  active  in  the  secondary  and  the  currents, 
s,  are  correspondingly  high  or  low.  The  crests,  however,  remain  appreciably 
unchanged  in  their  C  position;  i.  e.,  the  coefficients  of  inductance  remain  the 
same.  I  and  I'  are  nearly  equal,  L\  and  Lb  quite  different,  as  heretofore 
stated.  In  the  former  case  (/,  I'),  the  crest  is  an  extended  plateau. 


70 


ACOUSTIC  EXPERIMENTS  WITH  THE  PIN-HOLE 


If  we  regard  5  as  equivalent  to  current,  the  two  cases  may  be  described  as 

_s _ M.+Mb  s+s'  Ml 

s’  ~  Mi-Ms  °r  s-s'  ~Mb 

so  that  the  ratio  of  coefficients  of  mutual  induction  should  appear,  if  5  had 
been  standardized  in  terms  of  electrical  current. 

Figure  134  makes  a  comparison  of  the  currents  in  the  same  secondary 
(the  half-coil  of  Li),  if  in  one  case  the  current  is  cut  down  by  a  high  resistance 
(here  1,500  ohms),  curve  b,  and  in  the  other  left  without  resistance,  apart  from 


that  of  the  coils  themselves.  In  the  latter  case  the  fringe  displacement  is 
quite  out  of  the  field  of  view  (limit  about  5  =  140)  and  the  slide  micrometer 
must  be  used  to  restore  the  fringes.  This  involves  no  difficulty,  since  a  single 
new  fiducial  position  of  fringes  is  adequate  and  the  displacement  in  question  is 
read  off  on  the  micrometer.  The  distortion  of  curve  produced  by  the  resist¬ 
ance  is  striking,  so  that  the  crest  is  only  recognizable  with  difficulty  in  curve  b. 

In  figure  135  the  other  half-coil  of  Li  is  treated,  curve  a,  in  comparison 
(curve  6)  with  the  whole  coil  Li,  in  both  cases  without  additional  resistance. 
Naturally,  5  is  not  directly  proportional  to  the  currents.  The  sharpness  of 
both  crests  is  again  striking,  relatively  speaking.  In  curves  a,  figures  134 
and  135,  the  crests  are  at  C  =  o.i4  and  C  =  o.i3  microfarad,  respectively,  so 


PROBE  AND  THE  INTERFEROMETER  U-GAGE 


71 


far  as  determinable.  Since  the  pipe-note  is  d"\  or  =  io7  X  50.2,  the  coefficients 
for  the  half-coils  are  L\/ 2  =0.143  and  0.154  henry,  respectively.  The  crest 
of  the  full  coil,  L\,  is  at  C  —  0.07  microfarad,  so  that  L\  =  0.286  henry.  The 
difference  (0.143  +  0.154  —  0.286)  is  0.011  henry,  which  may  be  ascribed  to  the 
accessories  used  twice  in  the  former  case. 

60.  Primaries  in  parallel — Instead  of  cutting  down  the  secondary  current 
by  inserting  resistances,  R ,  until  the  fringes  remain  in  the  field  of  view,  as 
in  figure  134,  curve  b,  better  relations  are  to  be  anticipated  from  a  shunt  in 
the  primary,  P.  The  method  is  shown  in  the  insert,  figure  134,  where  R  is  the 
shunt.  Both  primaries  are  actuated  by  the  same  spring-break,  B ,  the  primary 
of  L1/2  being  in  parallel  with  P. 

Results  obtained  in  this  way  are  given  by  the  graphs  c  and  d  in  figure  134, 
for  two  different  values  of  R.  They  are  in  fact  less  distorted  than  curve  b  of 
the  same  figure.  A  surprise  was  encountered  in  computing  the  coefficient  L 
for  different  frequencies,  viz, 

d'n  o)2  =  5oXio6  Z1/2  =0.067  henry 

g"  22X106  0.15 

d "  12X106  0.268 

if  C  =  o.3  at  the  crests  as  the  graphs  c  and  d  imply.  Turning  to  figure  128, 
it  follows  that  the  poorly  developed  crest  g"  of  that  figure  must  have  been 
selected,  for  the  L1/2  value  is  then  of  the  right  order. 

These  results  make  it  desirable  to  ascertain  the  principle  underlying  the 
selection  of  harmonics  in  question.  Accordingly,  in  figure  136,  using  the  same 
method  with  primaries  in  parallel  (see  insert),  the  solution  is  attempted  by 
varying  the  resistance  of  the  shunt  from  R=  0°  to  R  =  1  ohm.  When  R=  & 
and  the  whole  current  is  therefore  sent  through  P2  as  well  as  Pi  (which  merely 
actuated  the  break  here),  the  crest  (7  =  0.15  (nearly)  does  indeed  require  the 
d'"  harmonic  in  the  pipe.  This  is  still  more  the  case  when  the  L1/2  coil 
(0.16  henry)  is  loaded  with  the  additional  small  inductance  of  coefficient 
Lb  —  0.02.  But  when  the  resistance  R  is  successively  decreased  (R=  100,  30, 
10,  5  ohms),  the  crest  is  at  C  —  0.3,  implying  the  harmonic  g"  in  the  pipe  as 
just  computed.  When  decreased  still  further  {R  —  2,  1  ohm),  the  crest  moves 
apparently  to  higher  (7  values  of  at  least  4  microfarads.  The  crest,  moreover, 
now  becomes  a  plateau  and  a  peak  can  not  be  identified.  If  d"  were  in  ques¬ 
tion,  the  C  should  be  about  0.5  microfarad,  which  the  graphs  do  not  fully 
admit.  It  is  possible  that  a  mixture  of  notes,  sometimes  d"  and  sometimes 
g",  may  supervene. 

However,  it  seems  clear  that  the  pitch  of  the  crest  depends  on  the  intensity 
of  current  in  the  primary,  P2,  and  increases  with  this  intensity.  It  requires 
vigorous  vibration  of  the  telephone-plate,  in  other  words,  to  shake  out  the 
df".  Otherwise,  with  dwindling  intensity,  g",  etc.,  will  appear  in  succession. 
This  was  curiously  substantiated  in  a  later  repetition  of  the  measurement  for 
R  =  co}  also  given  in  figure  136.  In  place  of  the  former  d'"  and  steep  crest, 
a  g"  note  with  rounded  crest  and  slowly  falling  curve  now  appears,  showing 
6 


72 


ACOUSTIC  EXPERIMENTS  WITH  THE  PIN-HOLE 


that  very  slight  modification  of  the  vibration  conditions  may  totally  change 
the  choice  of  the  pitch  of  the  vibration,  for  both  the  d'"  and  g",  when  once 
selected,  are  quite  persistent  throughout  the  remaining  test  on  a  given  day. 

To  return  to  the  difference  in  the  form  of  the  two  curves  for  R  =  co  in 
figure  136,  the  rapid  fall  from  d'"  in  one  case  and  the  very  deliberate  descent 
from  g"  in  the  other,  are  referable  to  the  rapid  change  of  pitch  in  the  former 

case,  compared  with  the  slow  change 
in  the  latter.  This  is  indicated  by 
the  resonance  note  corresponding  to 
(7  =  0.1,  0.2,  etc.,  recorded  at  the 
bottom  of  the  figure  and  holding 
for  all  curves  except  Li/2-\-Lb.  It 
thus  follows  that  the  cusps  in  the 
acoustic  survey  of  the  pitch  of  the 
pipe  (like  fig.  128)  are  virtually 
much  sharper  in  their  C  values  for 
the  case  of  d'"  than  for  lower  pitch, 
so  that  g"  can  be  stimulated  by  a 
wider  range  of  near  notes,  or  at  least 
of  C  values,  than  can  d"'. 

There  are,  however,  other  facts 
left  unexplained,  as,  for  instance, 
the  difference  in  form  of  the  curves 
R=  00  in  figure  136  compared  with 
the  corresponding  curves  without 
a  shunt,  figures  134a  and  135a,  for 
practically  the  same  conditions.  The 
latter  are  almost  symmetrical  and 
slender  as  compared  with  the  former. 
Quite  persistent  when  first  obtained,  they  could  not  be  reproduced.  The 
cause  lies  probably  in  the  spring  platinum-break,  which  incidentally  changes 
its  relatively  low  pitch  somewhat,  and  thereby  evokes  different  groups  of 
high  overtones  in  the  telephone-plate.  In  proportion  as  one  or  more  of  these 
correspond  to  the  pitch  and  overtones  of  the  pipe,  the  graphs  obtained  are 
more  salient.  Additional  light  will  be  thrown  on  the  subject  by  the  following 
chapter. 


CHAPTER  III 


MUTUAL  RELATIONS  OF  PIN-HOLE  PROBES.  QUILL-TUBES 

Bl.^Outer  pin-hole  of  the  pipe  enlarged — If  the  outer  pin-hole  of  the 
pipe  tt  (insert,  fig.  138)  connecting  the  telephones  is  removed  and  replaced  by 
an  -J-inch  stopcock  K,  the  inner  pin-hole  r  leading  to  the  U-gage,  U,  being  left 
in  place,  the  results  obtained  in  the  application  of  the  preceding  method  of 
C  variation  are  peculiar.  As  shown  by  the  adjoining  graph,  when  the  cock  is 


all  but  closed,  the  fringe  displacement  5  for  an  appropriate  C  value  is  quite 
marked,  but  rarely  more  than  about  one-fifth  of  what  the  pin-hole  removed 
would  have  given.  If  the  stopcock  is  now  gradually  opened,  the  fringe  dis¬ 
placement  drops  to  zero  and  may  even  become  negative.  On  opening  the  cock 
farther  from  this  minimum  degree,  the  5  values  rapidly  increase  to  a  value 
even  above  the  original  (crevice)  datum.  Thus  it  appears  as  if  the  effect  of 
the  crevice  were  at  first  like  that  of  pin-hole  r,  but  negative,  the  two  cooperat¬ 
ing  with  r  in  excess.  As  the  crevice  enlarges  slightly  its  reciprocal  potency 
diminishes  more  and  more,  passing  through  zero  and  therafter  counteracting 
r  or  even  exceeding  it  (negative  displacement  s).  After  this,  with  further 
widening  of  the  crevice,  the  K  effect  rapidly  vanishes  and  r  only  is  active. 
The  two  graphs  r  and  K  are  shown  in  the  insert,  where  5  =r-K ,  illustrate  this 
point  of  view.  The  behavior  of  the  crevice  is  naturally  very  variable.  Some¬ 
times  5  =  0  is  not  reached  and  5  is  always  a  positive  minimum. 

73 


74 


ACOUSTIC  EXPERIMENTS  WITH  THE  PIN-HOLE 


For  each  set  of  the  stopcock,  moreover,  the  5  values  pass  through  definite 
maxima  or  minima  with  C.  Negative  minima  were  usually  found  for  C 
varying  in  o.oi  microfarad  from  zero,  whereas  the  positive  maxima  occurred 
with  C  varying  in  o.i  microfarad  from  zero.  The  phenomenon  is  suggestive 
and  will  presently  be  specially  treated. 

Here,  figures  137  and  138,  I  wish  to  record  the  results  when  the  cock  K  is 
wide  open  (one-eighth  inch  bore)  and  when  it  is  quite  removed  (one-quarter 
inch  bore).  Figure  137  shows  the  fringe  displacements  with  the  coils  L1/2  and 
Lc  in  circuit,  the  primaries  and  secondaries  in  series,  the  primary  of  the  latter 
actuating  the  spring-break.  The  5  values  are  quite  marked,  but  three  or  four 
times  weaker  than  the  crest  found  with  the  absent  pin-hole  inserted.  Both 
curves,  though  different  in  form,  have  the  same  initial  crest  at  about  C  =  o.i 
microfarad.  This  is  a  d"'  if  L1/2  -f-  Lc  =  0.2  henry,  as  estimated.  The  graph 
for  one-eighth  inch  bore  shows  no  salient  features  thereafter;  but  the  other 
graph  (one-quarter  inch  bore),  which  now  exceeds  it,  passes  a  second  definite 
crest  at  C  =  0.7  microfarad,  about,  which  should  be  near  #g\  Naturally,  the 
pipe  with  these  two  different  holes  in  the  middle  has  different  pitches  for  the 
two  cases,  the  remarkable  feature  being  that  with  these  large  apertures  there 
should  be  any  middle  node  at  all. 

In  figure  138,  the  same  kind  of  experiments  are  carried  out  with  the  two 
halves  of  the  coil  Li,  only,  in  the  secondary.  The  graphs  are  now  totally 
different  in  shape  from  the  preceding.  Although  the  inductance  is  greater, 
there  is  no  initial  crest,  the  two  found  being  at  (7  =  0.3  and  £  =  0.5  microfarad, 
and  here  the  curve  with  the  one-eighth  inch  bore  or  opening  is  the  stronger. 
The  pitch  should  be  near  #c "  and  #g"  respectively.  In  the  latter  case,  the 
remote  crests  for  the  wide  tube  happen  to  coincide. 

Hence,  the  endeavor  to  reduce  excessive  fringe  displacement  5  by  enlarging 
the  outer  pin-hole  did  not  succeed,  the  graphs  being  exceedingly  complicated. 
The  phenomena  introduced  in  this  way,  however,  deserve  further  attention. 

52.  Reversal  of  outer  pin-hole  probe — In  figure  1396,  where  it'  is  the 

pipe  connecting  the  telephones  at  T  and  T\  the  pin-holes  r  and  5  are  set  to 
cooperate  with  each  other.  The  stream-lines  run  from  the  apex  to  the  base  of 
each  cone,  so  that  beyond  r  at  the  U-gage,  there  is  evidence  of  pressure. 
The  mean  density  of  the  node  between  r  and  5  is  an  excess.  Only  the  points 
of  the  pin-hole  cones  are  effective.  They  may  be  pricked  in  thin  metal  foil, 
and  will,  as  a  rule,  act  positively  or  negatively,  according  as  the  puncture 
is  carefully  made  from  within  or  from  without.  Size  of  hole  and  slope  of 
walls  may  be  important,  but  the  volume  of  the  region  in  which  the  action  is 
completed  is  astonishingly  small.  Roughly,  one  may  surmise  that  within  the 
apex  of  the  hollow  cone  there  is  marked  vorticity.  (cf.  §  88.) 

In  figure  139c,  the  adjustment  for  electric  oscillations  are  diagrammatically 
given  ( e  electromotive  force,  3  cells  with  resistance,  B  platinum  spring-break 
of  low  frequency,  P  primaries  in  series,  L  actuating  the  spring-break,  Li  is  the 
secondary,  with  capacity  C  and  telephones  T,  T\  connected  by  the  pipe  //'). 


PROBE  AND  THE  INTERFEROMETER  U-GAGE 


75 


Figure  140  shows  the  fringe  displacement  5  for  the  summational  adjust¬ 
ment  of  pin-holes,  when  the  capacity  in  the  secondary  is  varied  in  steps  of 
o.  1  microfarad.  There  is  a  maximum  at  C  =  0.3  microfarad  about,  correspond¬ 
ing  to  the  oscillation  pitch  near  d",  and  a  minimum  at  C  =  o.8  microfarad 
corresponding  to  at  which  the  pipe  makes  its  nearest  approach  to  silence, 
though  there  is  abundance  of  multiresonance  left  here.  Nevertheless,  the 


zr 


crest  for  £  =  0.3  and  the  trough  for  C  =  o.8  must  dominate  the  whole  of  the 
subsequent  experiments. 

The  lengths  of  the  pin-hole  pipes  (7,  lr)  in  the  summational  case  will  be 
treated  later. 

It  follows  that  if  the  pin-hole  probes,  r,  s,  are  adjusted  as  in  figure  1390 
(T,  V  telephones  in  phase,  it'  acoustic  pipe,  interferometer  U-gage  beyond 
U)  they  will  counteract  each  other.  The  effect  at  U  will  be  differential,  either 
a  pressure  or  a  dilatation,  according  to  the  relative  efficiency  of  the  pin-hole 

probes. 

The  inner  of  these,  r,  is  left  constant  in  quill-tube  length,  and  its  effect 
will  be  persistently  positive.  The  outer  pin-hole,  s  (fig.  i39a)»  carries  a 


76 


ACOUSTIC  EXPERIMENTS  WITH  THE  PIN-HOLE 


quill-tube  extention  Z,  of  variable  length.  Such  a  quill-tube  (Z)  as  heretofore 
shown,  is  a  musical  instrument  with  a  pin-hole  embouchure ;  but  the  effects 
obtained  in  the  present  paper  are  enormous  as  compared  with  the  older  evi¬ 
dence.*  It  is  presumable  that  the  effectiveness  of  5  and  also  of  r  will  depend 
on  the  frequency  of  the  note  of  the  pipe  tt'  primarily  (remembering  that  a 
telephone-plate  overtone  may  be  in  question)  and  on  the  natural  frequency 
of  the  pin-hole  quill-tube  secondarily. 

The  experiments  with  counteracting  pin-hole  probes  were  made,  as 
summarized  in  figures  141  and  142,  by  successively  increasing  the  length  of 
the  outer  pin-hole  tube  from  Z  =  4  to  Z  =  13  cm. ;  for  each  value  of  Z,  the  capacity 
C  was  changed  in  steps  of  0.01  microfarad  from  o  to  0.1  microfarad  (fig.  141), 
and  in  steps  of  0.1  microfarad,  from  o  to  1  microfarad  (fig.  142),  to  bring  out 
the  nature  of  the  phenomenon.  The  curves  show  that  an  even  wider  range  of  C 
would  have  been  desirable,  for  all  curves  seem  to  point  to  a  further  crest 
beyond  the  diagram.  The  length  of  the  quill-tube  prolonging  the  inner  pin¬ 
hole  r  was  kept  constant  throughout,  at  somewhat  above  Z'  =  10  cm. 

In  figure  141  for  Z  =  4  cm.  (length  of  quill  pin-hole  tube)  the  outer  pin-hole 
5  dominates,  the  curve  being  in  the  negative  or  dilatational  field  up  to  C  =  0.8 
microfarad.  There  is  a  well-developed  negative  crest  at  C  =  o.o4,  probably 
near  g'". 

When  Z  is  increased  to  8  cm.,  the  negative  crest  wanes,  falling  to  some¬ 
where  between  C  =  o.oi  and  C  =  o.o2  microfarad;  but  the  curve  soon  becomes 
strikingly  positive,  so  that  the  inner  pin-hole  r  prevails. 

The  further  increase  of  Z  to  13  cm.  of  length  shifts  the  curve  back  to  the 
negative  region.  There  is  now  no  discernible  crest,  but  all  negative  fringe 
displacements  are  very  large.  It  is  thus  probable  that  between  l  =  8  and  Z  —  13 
there  is  an  instability,  at  which  the  curve  drops  almost  suddenly  from  positive 
to  negative  (curve  1  =  13  is  not  liable  to  be  the  lowest)  regions.  Clearly  much 
smaller  steps  in  length  must  be  interpolated  if  the  nature  of  the  phenomena  is 
to  be  disclosed.  The  crests  of  figure  141  are  not  discernible  in  the  summational 
curve,  figure  140,  possibly  owing  to  the  extremely  rapid  changes  of  frequency. 

Figure  142  is  a  later  continuation  of  the  work  for  the  larger  ranges  of 
decreasing  frequency,  already  specified.  Comparing  it  with  figure  140,  we 
notice  a  distinct  tendency  to  reproduce  its  crest  and  trough.  This  is  obvious 
in  case  of  l  =  8  cm. ;  it  is  more  obscure  for  l  =  4  cm.  and  nearly  absent  at  Z  =  13 
cm.  The  secondary  phenomena  may  thus  be  of  prime  importance.  As  a 
rule  the  s  values  vary  more  markedly  in  the  lower  frequency  ranges  (C  =  o.  1 
to  1  microfarad)  than  in  the  higher  (C  =  o.oi  to  0.1  microfarad);  i.e.,  the  pin¬ 
hole  probe  seems  here  to  be  more  responsive. 

63.  The  same.  Cases  of  smaller  length  increments — Data  obtained  in 
the  same  manner  as  in  the  preceding  are  given  in  figures  143  to  146,  the  steps 
being  0.0 1  and  0.1  microfarad  respectively.  Figure  143  shows  that  whereas 
the  graphs  l  —  2,  3,  5,  7,  though  different  in  character,  follow  each  other  in 

*Camegie  Inst.  Wash.  Pub.  No.  310,  1921,  §  25;  No.  310,  Part  II,  1923,  §  5 


PROBE  AND  THE  INTERFEROMETER  U-GAGE 


77 


regular  succession  for  values  of  C  below  0.06  microfarad;  but  between  /  =  7 
and  l  —  9  cm.  there  is  instability,  so  that  the  former  graph  drops  over  a 
relatively  large  range  in  s,  from  positive  to  negative  values.  There  is  a  definite 
crest  for  l  =  7.  The  other  curves  run  into  a  plateau,  which  in  figure  144  appears 
merely  as  double  inflection.  Consequently,  in  the  latter  case,  the  interval 
0.1  to  0.2  microfarad  was  also  worked  out  in  steps  of  0.01,  but  no  ignored 
crests  were  detected.  In  figure  145  the  steps  of  l  are  taken  larger  to  show 
that  oscillation  of  graphs  has  not  ceased. 


Figures  144  and  146  clearly  indicate  that  all  the  graphs  are  dominated 
by  the  summational  curve  a  (pin-holes  in  series),  at  least  in  so  far  as  the  posi¬ 
tion  of  minima  is  concerned.  The  maxima,  however,  are  shifted  to  the  right, 
i.  e.}  to  lower  frequency,  as  if  the  pipe-note  had  flattened  from  d"  to  b'  or  more. 

In  figures  141  to  146  the  inner  pin-hole  prevails,  at  least  in  the  region  from 
C  =  o.i  to  C— 1.0  microfarad,  the  curves  tend  to  be  strongly  positive  through¬ 
out.  Search  was  therefore  made  for  an  outer  pin-hole  which  would  have  the 
same  negative  excess  qualities  if  placed  in  the  outer  position,  s  in  the  inserts. 
After  many  trials  one  only  (No.  II)  was  found.  The  fringe  displacement  with 
this  probe  was  much  more  sluggish  than  in  the  preceding  experiments,  indicat- 


78 


ACOUSTIC  EXPERIMENTS  WITH  THE  PIN-HOLE 


in g  a  pin-hole  of  much  finer  bore.  For  this  reason,  perhaps,  the  results 
obtained  (figs.  147  to  150)  are  less  incisive,  as  it  was  necessary  to  wait  some 
time  before  the  full  fringe  displacement  was  assured. 

In  figure  147,  for  steps  of  0.01  microfarad,  the  curves  1  =  2,  4,  6  cm.  are  a 
progression,  with  the  crests  moving  to  the  right.  After  this  there  is  an  insta¬ 
bility  with  a  drop  in  5  values  from  1  =  6  to  8  and  10,  the  crests  tending  to  the 
left.  In  the  former  cases,  the  inner  pin-hole  is  still  dominant,  but  ceases  to 
be  so  in  the  latter  (/  =  8,  10  cm.).  One  may  notice,  in  general,  that  positive 
tendencies  in  5  here  replace  negative  tendencies  in  figures  143  and  145. 

In  figure  148  for  C  =  0.1  to  1.1  microfarad,  the  resemblance  to  the  summa¬ 
tional  curve  (supplied  in  figure  1 50a)  is  practically  eliminated.  The  strong 
summational  crest  at  £  =  0.3  microfarad  is  obscurely  replaced  by  troughs,  if  at 


all.  The  trough  at  C  =  0.8  has  often  no  correspondence,  but  there  is  in  this 
region  a  shift  of  maxima.  The  intense  negative  characteristics  of  this  pin-hole 
for  l  =  8,  10  cm.,  are  remarkable.  They  are  borne  out  in  figure  1 50  for  l  =  1 1  cm. 

Remarks  of  the  same  nature  may  be  made  with  reference  to  figures  149 
and  150  for  a  larger  range  of  l  values  and  with  unbroken  quill-tubes.  The  s 
drop  from  1  =  6  cm.  to  11  cm.,  is  of  the  same  nature  and  the  curves  closely 
resemble  the  preceding  series,  though  the  experiments  were  made  later  with  a 
different  adjustment.  The  summational  crest  suggests  a  differential  trough 
(in  1  =  6  obscured  by  rapid  descent),  the  summational  trough  a  differential 
crest,  though  much  shifted.  The  drop  from  1  =  6  to  1 1  cm.  is  reconciled  only 
after  C  =  o.8  microfarad  is  passed. 

Unfortunately,  in  endeavoring  to  improve  this  pin-hole,  No.  II,  by  washing 
it,  the  negative  character  completely  vanished.  It  must  have  been  due, 
therefore,  to  something  like  atmospheric  accretions  accumulated  in  years,  by 
which  the  pin-hole  was  incidentally  constricted  in  such  a  way  to  give  it  its 


PROBE  AND  THE  INTERFEROMETER  U-GAGE 


79 


negative  quality.  The  attempts  to  reproduce  it  failed  throughout.  Other 
pin-holes  examined,  A,  B,  C ,  G,  etc.,  all  showed  the  customary  positive 
character.  D  was  a  wider  quill-tube  (diameter  5.5  mm.)  than  the  others 
(diameter  3.5  mm.),  and  with  this  its  isolated  behavior  may  be  associated. 
The  search  for  the  lost  negative  quality  in  short  pin-holes  like  No.  II  will  be 
undertaken  elsewhere  (cf.  §  88). 

A  more  systematic  and  extended  survey  with  the  modified  pin-hole  II 
is  given  in  figures  15 1  to  153,  on  the  same  plan  as  heretofore.  In  case  of  the 
lengths  of  pin-hole  tube,  1  =  2,  4,  6,  8,  (10)  cm.,  the  capacity  C,  was  varied  in 


steps  of  0.1  microfarad  only,  to  prevent  confusion  of  curves.  The  graphs 
rise  from  1  =  2  to  1  =  6 ,  the  latter  showing  exceptionally  high  5  values.  From 
1  =  6  to  l  =  8  cm.  there  is  a  vibrational  instability  in  the  quill-tube  and  a  con¬ 
sequent  drop  of  curve,  which  continues  to  /  =  (10)  cm. 

The  sectioned  tube  was  replaced  next  day  by  a  single  tube,  and  this  is 
recorded  in  an  even  lower  curve  at  1=  10.  Curves  (10)  and  10,  however, 
are  of  the  same  character,  and  the  difference  in  location  is  more  probably  due 
to  favorable  change  in  the  pitch  of  the  spring-break,  or  to  a  small  difference 
of  length.  The  series  /  =  ioto/  =  2o  cm.  is  given  both  for  AC  =  0.01  microfarad 
below  C  =  o.i  microfarad,  and  for  AC  =  0.1  microfarad  above  C  =  o.i  micro¬ 
farad.  In  figure  151  the  progressive  march  of  curves  upward  over  the  enor- 


80 


ACOUSTIC  EXPERIMENTS  WITH  THE  PIN-HOLE 


mous  5  interval  is  quite  remarkable;  but  after  Z  =  20,  the  curve  suddenly 
drops  again  to  the  marked  negative  s  values  of  /  =  22  cm.  A  second  vibra¬ 
tional  instability  has  thus  been  encountered.  The  same  routine  with  more 
complicated  graphs  is  seen  in  figure  153,  l  — 10  to  20  to  22  cm. 

The  experiments  were  then  pushed  farther  for  1  =  22,  24,  26,  29  cm.;  but 
to  retain  the  clearness  of  the  diagram,  only  the  latter  is  given.  The  graphs 
again  march  regularly  upward,  even  29  being,  as  yet,  far  from  the  goal  reached 
by  /  =  6  cm. 


Figure  152  is  the  summational  curve  for  pin-holes  in  series.  It  rises  to 
5  =  265,  about,  which  is  but  little  larger  than  the  combined  5  difference  between 
1  —  6  and  l  =  10,  about  As  =  1 50  —  ( — 100)  =  2  50  at  the  same  C. 

54.  Summary — It  is  difficult  to  specify  any  characteristic  of  these 
curves,  in  view  of  their  sinuosities.  As  a  whole  the  fringe  displacement  for 
C=o.i  microfarad  is  such  that  it  will  answer  the  purposes  of  discrimination, 
at  least  at  the  outset.  These  data  may  be  tabulated  as  follows: 

C  =  o.i  microfarad 


/  = . 24  6  8  10  12  14  16  18  20  22  29  cm. 

*  = . 63'  100  140  -33  {lj9°}-45  -35  -7  35  105  -57  30 


PROBE  AND  THE  INTERFEROMETER  U-GAGE 


81 


80 


40 


0 


154 

V 


20 


They  are  constructed  in  figure  154,  which  may  be  regarded  as  summary 
of  figures  151  to  153.  The  detailed  account  which  the  pin-hole  probe  gives 
of  the  nature  of  the  vibration  in  quill-tubes  is  thus  amazing.  Figure  154 
admits  of  a  straightforward  interpretation.  When  the  quill-tube  of  the  outer 
pin-hole  is  elongated,  the  vibration  for  a  given  harmonic  within  ceases  more 
and  more,  to  eventual  silence.  Hence  the  inner  or  positive  pin-hole  is  con¬ 
tinually  more  effective  to  a  positive  maximum.  After  this  the  outer  pin-hole 
vibration  drops  to  the  next  harmonic  of  lower  frequency.  Corresponding  to 
the  longer  tube,  the  outer  vibration  is  then  suddenly  intensified  and  is  in 
excess  of  the  inner  pin-hole  vibration.  Negative  values  of  s>  therefore,  super¬ 
vene,  to  be  gradually  diminished,  in  turn,  on  further  elongation  of  the  outer 
tube.  The  positive  increments  of  the  graph,  figure  154,  are  thus  continuous 
and  the  changes  gradual,  the  negative  increments  sudden,  and  the  action 
impulsive.  This  figure  and  others  of  a  similar  nature  shows  that  to  pass 
from  cusp  to  cusp  and  elonga¬ 
tion  of  quill-tube  of  about  14 
cm.  is  needed.  An  efficient 
probe  has  a  node  at  the  reen¬ 
trant  apex  of  the  pin-hole. 

The  above  work,  which 
encounters  the  superposition, 
more  or  less,  of  four  harmonic 
graphs,  those  of  the  electric 
oscillation  and  the  pipe  acoustic 
oscillation  and  those  of  the 
two  pin-hole  tubes  individu¬ 
ally,  is  naturally  destined  to 
run  into  complications.  It  was 
therefore  thought  best  to  avoid  theoretical  speculation.  The  abscissas, 
C  =  l/L(2Trn)2  =  \2/L( 2ttv)2,  increase  with  the  squares  of  period  or  wave¬ 
length.  Increasing  l  of  the  outer  pin-hole  increases  X.  If  a  C  is  found  to  fit 
it,  it  does  not  generally  fit  the  fixed  l'  of  the  inner  pin-hole  nor  the  pipe  tt'. 
There  is  a  further  outstanding  factor  in  the  fit  of  the  bore,  etc.,  of  the  pin¬ 
hole  to  the  note.  Finally,  overtones  in  the  telephone-plate  will  be  changed, 
with  small  changes  in  the  pitch  of  the  electric  spring-break. 

If  we  turn  back  to  figure  128,  giving  the  survey  in  pitch  of  the  tube  tt', 
we  are  struck  by  the  extremely  sharp  cusps  at  the  harmonics,  alternating 
with  intervals  of  complete  silence.  This  implies  the  use  of  a  motor  periodic 
break  of  variable  frequency.  In  contrast  with  this  succession  of  cusps,  such  a 
curve  as  figure  140,  obtained  with  the  spring-break  of  constant  low  pitch,  is 
illuminating.  The  tube  tt’  is  never  silent.  It  follows  that  high  harmonics 
fitting  the  pipe  tt'  must  be  shaken  out  of  the  telephone-plates  throughout  and 
in  succession,  each  in  turn  accentuated  by  the  pipe.  The  drop  of  curves 
observed  in  figures  143  and  147,  however,  is  probably  incident  in  the  quill- 
tube  itself,  additionally;  but  the  absence  of  silence  in  all  of  them  is  to  be 
referred  to  the  pipe  tt'. 


82 


ACOUSTIC  EXPERIMENTS  WITH  THE  PIN-HOLE 


It  follows  that  if  sharp  cusps  and  precise  values  of  L  or  C  are  to  be  ob¬ 
tained,  the  motor  periodic  break  will  have  to  be  used  in  connection  with  tt'. 

55.  Pin-holes  in  series.  Change  of  length  and  electric  capacity — It  has 

been  shown  in  the  preceding  paragraph  that  the  efficiency  of  a  pin-hole  probe 
(caet.  par.)  depends  essentially  on  the  quill-tube  length  and  that  the  response 
is  a  maximum  when  this  length  favors  the  occurrence  of  a  note  at  the  reentrant 
apex  of  the  cone.  It  is  desirable  to  test  this  inference  with  the  pin-holes  in 
series,  as  shown  in  the  insert  of  figure  155,  i.  e.y  to  prolong  both  l  and  l'  in 
definite  steps.  Figures  155  and  156,  made  with  pin-holes  No.  II  and  No.  Ill, 
respectively  (the  latter  poor  in  response),  have  a  preliminary  bearing  on  this 
inquiry.  In  figure  155,  the  original  length  is  1  =  2  cm.  and  the  corresponding 


harmonic  is  strong  (C  =  o.i  microfarad)  and  of  high  frequency  near  d'". 
Prolonging  the  quill-tube  to  1  =  6  cm.,  the  initial  harmonic  vanishes  and  is 
replaced  by  one  with  a  fiat  crest  at  C= 0.35  microfarad  near  g".  If  the  tube 
is  further  prolonged  to  l  =10  cm.,  the  high  frequency  crest  near  d'"  again 
appears.  All  the  graphs  give  evidence  of  the  minimum  between  C  =  0.6  and 
0.8  microfarad,  to  be  associated  with  the  pipe  tt'. 

In  figure  156,  the  pin-hole  tube  was  only  1  =  1  cm.  long;  but  for  1=  1  and 
3  cm.,  the  maximum  near  d'"  is  again  apparent.  Prolonging  the  tube  to 
5  cm.  or  to  7  cm.  deletes  the  crest  at  C  =  o.i  and  replaces  it  by  a  fiat  crest 
near  g"  ((7  =  0.35)  as  before. 

The  curves  for  increasing  length  l  in  general  show  reduced  5-values  in 
succession,  so  far  as  observed. 

The  elongation  of  the  quill-tube  l  is  an  enlargement  of  the  volume  of  the 
pipe  tt'  and  must  eventually  interfere  with  its  period.  This  is  a  complication 


PROBE  AND  THE  INTERFEROMETER  U-GAGE 


83 


which  makes  it  difficult  to  disentangle  the  curves,  and  the  graphs  of  the  syste¬ 
matic  work  are  therefore  omitted.  They  convey  no  information  beyond  the 
content  of  figures  156  and  157.  A  2 -cm.  addition  had  almost  no  effect. 
Naturally  the  larger  pipe,  tt',  dominates  the  small  cavity  of  /. 

The  tube  l  was  thereafter  elongated,  on  the  salient  side  of  the  probe, 
keeping  the  distance  of  the  pin-hole  from  tt'  constant.  These  additions  were 
also  ineffective  (to  5  cm.)  unless  they  were  very  long  (10  cm.),  thin  quill- 
tubes.  The  insensitiveness  of  the  pin-hole  probe  on  its  salient  side  to  these 
alterations  was  to  be  expected. 


Figures  157,  158  give  the  results  obtained  on  elongating  the  inner  probe 
(/'  in  the  insert) ,  leaving  the  pin-hole  r  in  place.  This  does  not  interfere  with 
the  volume  of  the  pipe  tt' .  The  tube  V  terminates  at  U,  the  large  cistern  of 
the  mercury  U-tube,  and  l'  can  not  therefore  be  decreased  much  below  7  cm. 
The  graphs  correspond  very  closely  to  an  inversion  of  figures  151  to  154;  e ., 
there  is  a  very  rapid  rise  from  /'  =  7  to  l'  =  go  cm.,  indicating  instability,  this 
time  of  a  positive  character  (see  fig.  158),  because  r  is  the  positive  pin-hole. 
From  lr  —  9  to  /'  =  i3  cm.  the  curves  descend  gradually,  as  the  r  effect  is 
diminished  by  the  absence  of  a  strong  node  at  the  pin-hole  until  the  next  rise 
appears  with  the  succeeding  harmonic.  The  crest  remains  at  C  =  0.1  through- 


84 


ACOUSTIC  EXPERIMENTS  WITH  THE  PIN-HOLE 


out  and  increases  enormously  in  sharpness  when  the  quill-tube  length  favor¬ 
able  to  the  particular  harmonic  in  question  is  attained. 

These  graphs  are  therefore  interesting,  as  they  suggest  a  reason  for  flat¬ 
ness  of  graphs  and  obscure  crests.  Thus  the  graph  for  /'  =  7  cm.  is  nearly 
without  marked  salience. 

The  endeavor  to  continue  this  work  for  greater  lengths,  l'  (figs.  159  and 
160),  ran  counter  to  an  incidental  break  of  pitch  from  about  d'"  to  d",  so  that 
a  continuous  curve  could  not  be  constructed.  Such  unfortunate  changes 
are  not  rare  and  seem  to  result  from  changes  of  temperature  modifying  the 
stresses  in  the  telephone-plates.  The  new  results  for  the  crests  at  C  =  0.25 
microfarad  are,  however,  consistent,  and  their  relation  to  l'  is  a  continued 
decrease  of  5  as  the  quill-pipe  joining  r  to  the  U-gage  reservoir  grows  longer. 
One  may  therefore  conclude  that  the  d!”  curve  of  figure  158,  if  it  could  have 
been  prolonged,  would  continually  descend  from  a  general  maximum  of 
about  V  —  9  cm.  This  is  therefore  here  the  best  length  for  the  junction. 

56.  Effect  of  the  number  of  pin-holes — 'Notwithstanding  a  number  of 
investigations  with  the  same  bearing  made  in  the  earlier  work,*  the  precise 
cause  of  the  positive  or  negative  quality  of  the  pin-hole  remains  obscure. 
Inverting  the  pin-hole  probe  usually  changes  this  quality,  though  it  does  not 
always  pass  from  positive  (fringe  displacement,  +5)  to  negative  (—5).  I 
have  supposed  that  the  slope  of  the  pin-hole  walls  might  here  be  discriminat¬ 
ing,  the  stream-lines  passing  from  the  apex  to  the  base  of  the  hollow  cone. 
This  suggests  itself  for  a  pin-hole  made  of  a  constricted  glass  quill-tube.  But 
as  the  pin-hole  may  be  made  quite  as  efficiently  by  merely  puncturing  a  piece 
of  metal  foil  (cemented  to  the  end  of  the  tube),  either  from  within  or  from 
without,  by  a  fine  needle,  the  explanation  given  seems  to  be  inadequate. 
One  might  therefore  suppose  that  the  inside  of  the  probe,  when  it  holds  a 
node,  is  necessarily  at  higher  pressure  than  exists  on  the  salient  side  or  in  the 
free  air,  for  reasons  similar  to  those  suggested  by  Bernoulli’s  principle.  A 
vibrating  column  necessarily  holds  an  excess  of  energy  per  cubic  centimeter 
compared  with  the  still  air  outside.  In  such  a  case  the  inversion  of  the  pin¬ 
hole  tube  should  change  the  sign  of  its  quality;  but  this  also  is  not  always  the 
case.  Nodes,  moreover,  may  be  present  on  both  sides. 

As  the  question  is  thus  open,  I  have  thought  it  desirable  to  begin  a  syste¬ 
matic  investigation  by  the  present  methods,  and  figures  163  and  164  show 
the  effect  of  increasing  the  number  of  pin-holes  of  about  the  same  size,  etc., 
punctured  from  without  (see  insert,  fig.  163,  showing  pin-holes  in  the  plate  p 
on  the  quill-tube  q).  The  results  are  again  in  marked  degree  periodic.  With 
one  and  two  pin-holes  the  d"  crest  is  prominent,  but  after  this  the  d'"  crest  pre¬ 
vails.  The  sensitiveness  or  acoustic  pressure  5  is  decreasing  in  cases  corre¬ 
sponding  to  from  one  to  three  pin-holes  (fig.  164),  then  rapidly  increasing 
from  three  to  seven  pin-holes,  decreasing  again  from  seven  to  eight  pin-holes, 
and  thereafter  increasing  to  nine  pin-holes  or  over.  The  plate  was  then 

*Camegie  Inst.  Wash.  Pub.  No.  310,  1921,  §  1,  18 


PROBE  AND  THE  INTERFEROMETER  U-GAGE 


85 


removed  and  the  clear  quill-tube  ( q )  used  above.  The  acoustic  pressure,  s , 
is  now  a  maximum  and  exceptionally  high.  Finally,  the  quill-tube  itself  was 
removed,  leaving  a  round  one-quarter  inch  opening  in  the  pipe  tt',  opposite  the 
inner  probe  r.  The  acoustic  pressure,  5,  at  once  drops  enormously.  In  a 
measure,  this  would  be  expected  from  the  weakened  node  in  tt'f  even  though 
the  pitch  drops  also.  Notwithstanding  the  complicated  relations,  the  curves 
are  consistent. 


These  results  are  throughout  surprising.  The  probe  r  being  left  unchanged, 
a  positive  contribution  in  s  must  be  supplied  by  the  plate  p.  It  is  probable 
that  this  is  done  by  tuning  tt\  until  the  node  within  r  is  most  intense.  This 
occurs  ultimately  when  p  is  quite  removed. 

A  variety  of  experiments  was  made  with  extremely  fine  pin-holes.  Such 
observations  have  to  contend  with  the  difficulty  that  the  fringe  displacements 
are  very  sluggish.  It  is  necessary  to  wait  some  time  before  the  full  displace¬ 
ment  is  approached,  and  one  is  never  sure  that  it  has  been.  In  fine  single 
pin-holes  the  maximum  5  is  usually  reached  by  a  rapid  upward  trend  at 
C  =  o.i,  and  thereafter  the  curve  meanders.  Naturally,  the  quills  should  be 


86 


ACOUSTIC  EXPERIMENTS  WITH  THE  PIN-HOLE 


of  constant  length,  preferably  1  =  2  cm.  It  is  with  these  fine  pin-holes  that 
negative  displacement  is  most  frequently  in  evidence  when  the  quill  is 
reversed,  so  that  the  puncture  is  inward,  as  at  pr,  in  comparison  with  p, 
figure  165. 

Figure  165  is  a  record  of  three  identical  probes,  identically  punctured  so 
far  as  possible.  In  case  of  No.  1,  both  displacements  s  are  positive;  but  curi¬ 
ously  enough,  the  reentrant  adjustment  (p')  is  ahead  of  the  salient  adjustment 


( p ) .  This  shows  that  the  mere  reversal  of  the  tube  does  not  suffice  to  reverse 
the  sign  of  5,  but  that  some  additional  quality  of  the  pin-hole  itself  is  in 
question.  In  No.  2,  the  salient  5  values  are  far  in  excess  of  the  reentrant 
values.  The  latter  are  in  general  positive,  though  they  begin  with  a  negative 
hook.  In  No.  3,  the  salient  5  values  are  positive  but  weak;  the  reentrant 
values  are  now  persistently  negative,  the  curve  after  C  =  o.i  microfarad, 
terminating  in  a  plateau.  The  shoulder  of  this  curve  is  near  d!"  in  pitch,  like 
the  more  pronounced  cases  Nos.  1  and  2.  In  contrast  with  this,  the  crests 
of  the  curves  for  salient  cases  are  in  relatively  low  pitch,  if  crests  are  present 
at  all. 


PROBE  AND  THE  INTERFEROMETER  U-GAGE 


87 


The  three  probes,  though  nominally  identical,  differ  in  behavior  for  reasons 
which  one  can  not  even  conjecture.  It  is  probable  that  No.  3  (negative  case) 
is  the  finest  hole.  It  is  noticeable  that  the  reentrant  cases  fall  from  positive 
toward  negative  much  more  rapidly  than  the  salient  cases,  which  accounts 
for  the  reversal  in  case  No.  1.  A  comparison  of  salient  (sa)  and  reentrant  (sr) 
5  value  at  C  —  o.  1  microfarad  is  given  (scale  reduced  one-half  in  the  auxiliary 
curve  of  figure  165.  The  data  are  clearly  related;  a  pin-hole  which  has  the 
negative  quality  shows  it  in  both  the  salient  and  reentrant  adjustments. 

Unless  the  foils  p  are  punctured  alike  and  with  the  same  needle,  the 
relation  of  sa  and  sr  exhibited  in  figure  165  ceases  to  hold.  In  an  extended 
series  of  measurements  (Cs  graphs  from  C  —  o  to  0.5  microfarad,  which  must 
be  omitted  here),  14  pin-hole  probes,  all  2 
cm.  long,  were  selected  at  random.  Nos.  1 
to  10  were  quill- tubes  carrying  punctured 
plates;  B,  a  thin  brass  tube;  I,  II,  III,  the 


above.  The  graphs  obtained  all  shouldered 
at  C—  o.  1  microfarad  and  then  reached  a 
flat  maximum  at  C— 0.3  to  C— 0.4  micro¬ 
farad.  The  relations  of  sr  and  sa  for  C  =  o.i 
are  summarized  in  figure  166.  One  notes 
that  for  Nos.  1,  5,  7,  8,  and  9,  sr/sa  =  1.1; 
for  Nos.  B ,  3,  6,  sr/sa  =  0.9;  for  Nos.  2,  4, 

/,  sr/sa  =  0.7,  and  here  the  first  glass 
cone  is  included;  for  Nos.  10,  II,  III, 
sr/sa  —  0.4,  the  last  results  being  straggling, 
and  the  brass  probe  No.  10  is  classified  with 
the  glass  cones  II  and  III.  It  is  impos¬ 
sible  to  suggest  any  reason  for  the  occur¬ 
rence  of  these  groups  from  an  inspection 
of  the  pin-holes.  The  arrangement  would 
not  have  been  very  different  at  other  C  values.  Thus  at  the  crest  C  =  0.3 
to  0.4  microfarad,  the  data  found  are  recorded  in  figure  167.  We  have  the 
same  groups  with  No.  7  more  nearly  in  place,  granting  that  the  groups  are 
probably  quite  incidental.  In  case  of  Nos.  I,  II,  III,  and  10,  the  Cs  graphs 
were  definite  and  similar;  but  this  does  not  prevent  I  from  falling  into  the 
higher  group.  Many  of  the  punctures  were  very  fine  and  displacements 
sluggish  (particularly  6,  8,  9;  1,  2,  3).  In  §  90  this  complicated  subject  is 
taken  up  again  from  a  different  line  of  approach  and  with  better  success. 


5/ 

/  y 

'cA 

L 

Jm 

c 

Us 

y / 

7  0 

LX 

so 

// 

V— 

1  ( 

>6 

u 

/  6y 
So  y. 

5/ 

V 

/ 

- 

- N 

•  /  1/  y' 

^1  1 

u 

>7 

0  8  16  24  %2  40  48 

57.  Outer  quill-tubes  of  varying  lengths,  all  open — The  astonishing 
effect  produced  (fig.  163)  by  an  open  quill-tube,  1  to  2  cm.  long,  induced  me 
to  develop  this  result  further,  as  shown  in  figures  16 1  and  162.  It  seemed 
probable  that  a  node  in  the  middle  of  the  quill  l  might  cause  this  pipe  to  act 
as  if  it  were  constricted  there.  One  observes  that  lengths  from  /  =  2  to  6  cm. 

7 


88 


ACOUSTIC  EXPERIMENTS  WITH  THE  PIN-HOLE 


maintain  the  crest  at  d!" .  At  /  =  8  cm.  it  is  developing  at  d'\  which  seems  to 
be  retained  thereafter,  though  at  Z  =  13  cm.  the  crest  has  merged  into  a  prac¬ 
tically  even  plateau.  With  the  exception  of  the  kink  at  l  =  8  cm.  the  effect  of 
the  tube-length  l  is  a  rapid  decrease  of  acoustic  pressure  or  fringe  displace¬ 
ment  s,  quite  contrary  to  what  one  would  have  expected.  It  seems  as  if  the 
node  within  r  were  promoted  by  high  pitch  and  therefore  a  short  pipe  l. 
The  long  quill-tube  l  thus  acts  similarly  to  a  few  holes  in  the  plate  p,  figures 
163  and  164,  i.  e.,  figure  162,  if  reversed,  would  qualitatively  reproduce  the 
initial  part  of  figure  164.  In  figure  16 1  the  straight  fall  of  curve  from  the 
crest  at  1  =  2  and  6  are  noteworthy. 

Figure  161,  moreover,  suggests  reasons  for  the  frequent  occurrence  of 
plateau-like  maxima.  It  is  probably  associated  with  friction  in  the  long  quill- 
tube.  The  tube  responds  weakly  with  either  d"  or  dn\  no  matter  what  the 
excitation  pitch.  Excited  with  d"  it  may  sound  d'". 


Some  time  after  the  initial  datum  for  a  quill-tube  l  =  i  cm.  in  figure  162 
was  supplied  and  reduced  to  the  same  scale.  This  indicates  the  occurrence  of 
a  crest  at  1  =  2  cm.,  unless  the  short  tube-length  (1  cm.)  weakens  the  node  in 
tt'  disproportionately.  Finally,  for  l  =  o  cm.  (quill  adjutage  q  off)  the  datum  of 
figure  164  may  be  taken;  so  that  figure  162  exhibits  the  quill-tube  effect 
fully.  Such  adjutages  are  effective  for  a  mean  range  of  length,  say  between 
1  cm.  and  10  cm.  On  either  side  of  this  the  acoustic  pressure  (5)  rapidly 
falls  off  to  low  values.  (Cf.  §  60.) 

58.  Data  for  identical  reentrant  plate  pin-hole  probes  of  different 
lengths — Plate  (punctured  copper  foil)  pin-holes  are  not  usually  as  sensitive 
as  the  glass  cones  carefully  adjusted;  but  the  acoustic  pressures  appear  none 
the  less  clearly.  In  figures  168,  169,  and  170  I  have  recorded  the  results  of  an 
incidental  series  of  experiments  which  came  out  very  satisfactorily  and  gives 
new  information.  The  adjustment  is  shown  in  the  insert  figures  168  or  170, 
where  p  is  the  plate. 


PROBE  AND  THE  INTERFEROMETER  U-GAGE 


89 


In  the  present  experiments,  V  was  left  constant  and  about  6  to  7  cm.  long, 
while  the  length  of  l  was  successively  varied  from  l  =  2  to  l  =  24  cm.  On  vary¬ 
ing  C  (for  each  length)  from  C  =  o.o2  to  C=i.i  microfarads,  the  graphs  of 
figures  168  and  169  were  obtained.  These  are  so  full  of  detail  that  to  obviate  a 
bewildering  diagram  of  interlacing  curves  the  two  zero-lines  of  the  graphs 
have  been  successively  raised,  5=  10  or  20  scale-parts.  Since  all  curves  begin 
with  5  =  0  and  the  zero-line  is  further  shown  at  the  end,  this  vertical  displace¬ 
ment  of  graphs  need  not  be  confusing. 


A  great  variety  of  primary  and  secondary  troughs  and  crests  occur  in 
which  some  of  the  ornamentation  may  be  due  to  failures  of  the  telephone- 
plate  to  deliver  the  overtone  needed.  At  the  higher  pitches  (£<0.5  micro¬ 
farad)  the  acoustic  pressures  5  of  the  graphs  are  prevailingly  negative,  at 
lower  pitches  (O0.5  microfarad)  prevailingly  positive;  but  when  l  exceeds 
10  cm.,  graphs  in  the  negative  region  (dilatations)  are  the  rule. 

So  far  as  the  crests  can  be  specified,  they  are  given  in  the  following  table. 
When  l  exceeds  1 2  cm.  the  curves  are  liable  to  meander. 


2 

4 

6 

8 

10 

12 

15 

17 

24 

c 

s 

C 

s 

C 

s 

C 

5 

c 

5 

c 

s 

c 

5 

c 

5 

c 

s 

First  crest . . . . 

O.05 

.07 

0-35 

O.50 

0-75 

4-10 
-52 
-  4 
-15 
T40 

0.02 

0.07 

0.30 

0.5? 

O.9O 

4-  5 
-50 
—  16 
—20 

4-25 

First  trough  . . 
Second  crest . . 
Second  trough 
Third  crest . . . 

0.15 

0.40 

0.55 

0.80 

“45 
—  20 

-35 

+20 

0.06 

0.20 

0.30 

0-75 

-  5 
4-15 
4-io 
+72 

0.08 
0.50 
0.8? 
1. 00 

—62 

-37 

-47 

-43 

0.05 

0.15 

0.35 

0.70 

“45 

-27 

-38 

-19 

0.10 

0.65 

-47 

-  4 

O.II 

0.45 

0.6? 

0.7? 

-5i 

—  20 

—  26 

-25 

0.07 

0.55 

-43 

4-  7 

The  second  row  of  troughs  and  the  last  row  of  crests  are  the  most  out¬ 
standing,  and  they  have  been  reconstructed  in  figure  170,  showing  the  acoustic 
pressures  5  for  the  successive  lengths  of  quill-tube  l.  The  troughs,  curve  t , 
are  throughout  negative  (dilatation),  the  crests,  curve  c,  at  first  strongly 
positive  (pressures),  but  thereafter  also  negative.  The  little  hooked  crests, 
curve  a,  at  the  beginning  (£<0.05  microfarad),  are  found  in  1  =  4,  6,  and  8 
cm.  only.  This  little  graph,  a,  may  be  regarded  as  an  inversion  of  graphs  c 


90 


ACOUSTIC  EXPERIMENTS  WITH  THE  PIN-HOLE 


and  t.  The  pitch  of  the  crests  lies  between  C—  0.7  and  0.9  microfarad,  shift¬ 
ing  from  /'  to  e'  roughly.  The  pitch  of  the  troughs  shifts  relatively  much 
more,  say  from  (7  =  0.05  to  0.15  microfarad,  almost  from  /"'  to  f". 

Notwithstanding  this  vagueness  in  pitch,  the  interpretation  of  the  phe¬ 
nomena  given  by  figure  170  is  very  clear,  the  graph  for  troughs  corroborating 
the  graph  for  crests,  acoustic  pressures  are  a  maximum  when  roughly  1  =  7, 
14,  probably  21  cm.  and  minima  for  1  =  9,  18,  etc.,  i.  e.y  for  mid- values  of  l 
between  the  maxima.  It  is  particularly  remarkable  that  the  troughs  are  least 
dilatational  at  the  l  values  of  the  maxima  of  the  crest  graph. 

Furthermore,  since  the  inner  quill-tube  length  is  Z'  =  6  to  7  cm.,  one  may 
infer  that  the  maxima  of  figure  170  occur  when  (see  insert,  fig.  170)  l  —  l\ 
l  —  2l\  etc.  Hence  the  pipe  ttf  is  here  most  efficient  in  producing  acoustic 
pressure  (caet.  par.)  when  the  quill-tubes  l  and  V  are  equal  in  length.  This 

high  acoustic  pressure,  s,  occurring  in 
cases  of  geometric  similarity  of  the 
pipes,  is  probably  an  important  result, 
remembering  that  l  carries  the  re¬ 
entrant  pin-hole  and  is  a  closed  organ- 
pipe,  while  /'  is  an  open  organ-pipe. 
The  nodes,  which  are  to  be  located  in 
the  middle  of  V  and  at  the  p  end  of  l, 
should  in  cases  of  maximum  acoustic 
pressure  have  the  highest  excess  density 
over  atmospheric  density,  or  again,  the 
least  density  deficiency. 

If  we  regard  l'  as  an  open  pipe  and 
l  as  a  closed  organ-pipe  (in  virtue  of 
the  plate  pin-hole)  then  a  wave-length 
which  fits  the  former  tube-length  will  not  as  a  rule  fit  the  latter,  for  the 
closed  pipe  should  be  half  as  long  as  the  open,  for  the  same  fundamental 
pitch.  Hence  at  1  =  6  cm.,  if  the  inner  quill-tube  is  most  active,  the  outer 
should  be  least  so.  Acoustic  pressure  should  therefore  result,  if  we  postulate 
(§  60)  that  the  stream-lines  pass  from  it’  to  U  in  this  case.  If  the  pin-hole 
p  is  most  active,  they  pass  from  U  to  ttf  into  the  atmosphere  (dilatation). 

Inasmuch  as  the  overtones  of  the  quill-tubes  must  also  be  similarly  treated, 
a  diagram,  like  figure  171,  will  assist  in  locating  the  positions  of  crests  and 
troughs  in  such  graphs  as  figures  168  to  170.  In  figure  171  the  lengths  of 
quill-tubes  l,  V  are  laid  off  horizontally,  the  corresponding  wave-lengths  X, 
X',  resonantly  sustained  by  the  tubes,  vertically.  In  the  experiments,  /'  =  6 
nearly,  is  kept  constant.  Hence  the  wave-lengths  in  question  are  suggested 
by  the  horizontals  marked  X'  =  i2,  6,  4,  etc.  On  the  other  hand,  l  is  varied, 
the  oblique  lines  marked  X  =  4 /,  4Z/3,  etc.,  suggest  the  resonant  wave-lengths 
possible  in  the  pin-hole  tube.  Now,  as  l  was  increased  in  steps  of  2  cm. 
(Z  =  2,  4,  6  cm.,  etc.),  the  verticals  at  these  points,  at  their  intersection  with  the 
horizontal  and  oblique  lines,  will  point  out  the  resonant  wave-lengths  to  be 


PROBE  AND  THE  INTERFEROMETER  U-GAGE 


91 


expected.  These  intersections  have  been  accentuated  in  figure  17 1  by  open 
circles  for  crests  and  closed  circles  for  troughs. 

Suppose,  now,  we  let  the  impressed  wave-length  \c,  due  to  the  electric 
oscillation,  diminish  from  a  high  value  ( C  large)  to  zero,  at  1  =  6  cm.,  for  in¬ 
stance.  We  should  first  encounter  a  trough  above  the  diagram  at  the  inter- 
section-point  of  X  =  4/.  This  trough  is  also  implied  in  the  graph  1  —  6  of 
figure  168,  beyond  the  diagram  on  the  right.  Next  we  encounter  the  funda¬ 
mental  crest  at  a ,  figure  171,  strongly  marked  in  figure  168.  We  then  reach, 
in  succession,  trough  b,  crest  c,  trough  d ,  crest  e,  etc.,  alternations  quite 
like  the  graph  6  in  figure  168,  when  c  decreases.  Below  e  the  overtones  will 


0A  •/  £  -3  -4.  -5  -6  -7  '8  *0  1-imf. 

0-0  1  23  4-5  I 


naturally  be  more  and  more  vague  or  nonexistent.  This  also  is  borne  out 
by  figure  168. 

Finally,  it  is  not  necessary  that  trough  and  crest  should  alternate.  For 
instance,  if  l  =  4  in  figure  17 1,  the  trough  /  is  followed  by  crest  g  and  crest  h 
before  the  next  trough,  i,  appears,  followed  by  the  crest  j.  Below  this  there 
is  further  interference.  This  lack  of  rhythm  is  also  a  marked  feature  in  the 
graphs,  figure  168,  et  seq. 

To  work  out  a  scheme  of  this  kind  quantitatively  would  be  difficult,  because 
the  overtones  of  the  telephone-plate  are  a  further  powerful  interference,  the 
importance  of  which  would  first  have  to  be  estimated.  For  the  present  it  is 
more  urgent  to  see  in  how  far  similar  acoustic  pressures  may  be  produced 
quite  without  pin-holes.  This  is  done  in  paragraph  60,  where  the  fringes  are 
to  be  enlarged  in  the  interest  of  greater  5  values  for  the  smaller  pressures 
anticipated. 


92 


ACOUSTIC  EXPERIMENTS  WITH  THE  PIN-HOLE 


59.  Inner  quill  and  outer  conical  glass  pin-hole — To  estimate  the  relative 
intensity  of  the  present  acoustic  pressures,  the  experiments  of  figure  172, 
were  added.  Here  the  outer  tube  (see  inserts)  is  the  glass  pin-hole  probe,  IV, 
(heretofore  used  within)  and  the  inner  tube  is  a  clear  quill,  6  to  7  cm.  long. 
These  experiments  are  thus  an  inversion  of  the  set  given  in  figures  16 1  and 
162,  in  which  the  pin-hole  is  located  within,  with  an  outer  quill.  In  figure  172, 
when  the  outer  pin-hole  is  salient,  the  acoustic  pressures  are  positive  with 
crests  at  C— 0.3  and  0.93  microfarad  and  a  trough  at  0.47.  They  are  much  in 
excess  of  the  reentrant  case,  in  which  the  pressures  are  negative  (dilatations) 
with  (negative)  crests  at  C=o.i,  0.47,  and  1.1  microfarad,  and  troughs  at 
C  —  o.2  (?)  and  0.7  microfarad.  Since  the  reentrant  curve  is  inverted,  troughs 


correspond  to  crests  and  vice  versa  in  the  two  curves  in  question.  Hence  at 
C  =  o.47,  the  two  troughs  (salient  and  reentrant)  coincide  in  their  C  position; 
but  the  crests  in  the  reentrant  curve  are  shifted  from  C  =  o.3  to  0.1  and 
from  (7  =  0.93  to  0.7  microfarad.  Beyond  C  =  1.1  microfarads  there  is  prob¬ 
ably  further  coincidence  of  troughs,  and  one  is  inclined  to  associate  them 
with  the  tt'  pipe.  The  two  graphs  thus  depart  from  each  other  in  the 
location  of  crests  different  from  the  set  in  figure  161,  except  in  the  location 
of  the  C=o.3  crest.  They  are,  moreover,  far  below  the  latter  in  range  of 
pressures,  though  here  a  variation  of  the  l'  values  should  first  be  tested  for 
favorable  pairs  of  l  and  l'  lengths.  The  extent  to  which  the  glass  pin-hole 
curves  exceed  the  plate  pin-hole  graphs  is  shown  by  the  highest  graph  for  the 
latter  (/  =  /'  =  6  cm.)  at  the  bottom  of  figure  172. 

If  the  two  pin-holes  were  to  cooperate,  i.  e.,  be  used  in  series,  the  upper 


PROBE  AND  THE  INTERFEROMETER  U-GAGE 


93 


graph  of  figure  172  would  be  expected.  This  is  again  quite  different  from  the 
preceding,  with  crests  at  £=0.4  and  1.0  microfarad. 

The  dissimilarity  of  curves  in  figures  16 1  and  172  is  astonishing,  even  if 
different  telephonic  overtones  should  have  been  incidentally  awakened.  It 
seems,  therefore,  as  if  the  quill-tube  l',  which  terminates  in  the  capacious  but 
closed  U-tube  reservoir  (10  cm.  diameter,  1  cm.  deep)  is  not  to  the  same 
extent  free  as  the  quill-tube  /,  which  terminates  in  the  atmosphere. 

60.  Cooperating  quill-tubes  without  pin-holes — In  the  preceding  para¬ 
graphs  counteracting  pin-hole  probes  of  successively  different  lengths,  as  well 
as  pin-hole  probes  of  different  lengths,  in  series,  were  tried  out,  with  the  results 
that  the  acoustic  pressure  varied  with  length  periodically,  in  the  manner  stated. 

The  outer  (salient)  pin-hole  was  then  removed  and  replaced  by  a  .suc¬ 
cession  of  clear-bore  quill-tubes.  Periodic  results  of  the  same  nature,  varying 
with  the  length  of  the  other  quill-tube,  were  again  obtained,  and  under  favor¬ 
able  length  adjustments  the  highest  acoustic  pressures  hitherto  detected 
(same  scale  for  s  throughout)  were  recorded. 

It  is  natural,  therefore,  to  remove  both  pin-holes,  to  replace  them  by 
clear  quill-tubes  of  lengths  l  and  V ,  as  in  figure  173,  V  communicating  with 
the  capacious  reservoir,  U ,  of  the  interferometer  U-gage.  The  acoustic  pipe 
tt'  is  actuated  by  telephone-plates  near  its  ends,  to  which  the  telephones  are 
sealed.  Hence  tt'  may  be  regarded  as  communicating  freely  with  air,  at  the 
farther  ends  of  l  and  for  though  U  is  closed,  it  is  about  10  cm.  in  diameter 
and  1  cm.  deep. 

Owing  to  the  small  acoustic  pressures  to  be  expected,  the  fringes  of  the 
interferometer  were  enlarged  more  than  twofold.  Hence  the  5  values  of  the 
graphs  are  correspondingly  magnified. 

In  the  experiments  given  in  figure  174,  the  inner  quill  was  left  constant 
at  /'  =  10  cm.  while  the  outer  was  varied  from  l  =  o  to  /  =  7  cm.  No  fringe  dis¬ 
placements,  5,  were  obtained  at  l  =  o  (one-quarter  inch  tubulure  in  tt')  nor 
above  l  =  5  cm.  of  quill-tube  length,  l. 

The  curve  ( l '  =  10)  on  the  left  records  two  sharp  cusps  at  l  =  i  and  3  cm.,  a 
curious  result  to  be  interpreted  by  the  aid  of  the  curves  on  the  right,  in  which 
C  is  varied  from  0.4  to  1.1  microfarads  for  each  value  of  l. 

The  C  graphs  for  l  =  i  cm.  are  different  in  type  from  the  others  (1  =  2,  3, 
4  cm.),  showing  a  well-developed  crest  at  C  =  0.75  microfarad.  They  change 
in  value  with  slight  differences  of  adjustment  of  the  short  quill-tube,  l=i  cm., 
so  that  two  graphs  are  given  as  examples.  On  the  other  hand,  from  1  =  2  cm., 
which  is  again  low  in  5,  the  graphs  rise  with  great  rapidity  to  the  graph  for 
/  =  3  cm.  Again,  two  curves,  /  =  3  and  1=  (3),  are  given,  the  change  being  due 
to  slight  alterations  in  the  insertion  of  the  3 -cm.  quill-tube.  From  the  high 
values  of  acoustic  pressure,  s,  for  l  =  s,  the  graphs  fall  again  to  the  low  values 
for  l  =  4  cm.  and  to  zero  at  /  =  5  cm.  This  curious  kind  of  variation,  as  exhib¬ 
ited  in  the  graph  l'=io  cm.,  may  be  referable  to  two  independent  crests 
superposed. 


94 


ACOUSTIC  EXPERIMENTS  WITH  THE  PIN-HOLE 


The  acoustic  pressures,  s,  are  always  positive,  showing  that  the  V  quill  is 
dominant;  but  for  Z  =  o  and  Z  above  5  cm.  all  acoustic  pressure  vanishes.  The 
very  steep  cusps  of  the  V  l  graph  indicate  the  great  delicacy  of  vibrational 
equilibrium.  It  is  difficult  to  reinsert  the  outer  quill  so  as  to  quite  reproduce 
an  original  graph. 

In  figure  175  the  conditions  are  reversed;  the  outer  quill  is  kept  constant 
at  /  =  3  cm.  (favorable  length  in  fig.  174),  while  the  inner  quill  is  extended  from 
Z  =  otoZ  =  i6,  in  steps  of  2  cm.  In  the  C  graphs  on  the  right  of  figure  175  there 
is  an  accelerated  rise  of  acoustic  pressure,  s,  between  V  —  o  and  V  =  6  cm.  A 
maximum  of  s  values  is  reached  at  about  Z'  =  10  cm.  Thereafter  the  5  values 
gradually  fall  again  with  changes  in  the  form  of  the  C  graphs.  The  variations 
as  a  whole  are  exhibited  in  the  slf  graph  1  =  3  on  the  left  side  of  figure  175. 
The  present  phenomena  are  therefore  more  uniform  in  character  than  those 
of  the  preceding  figure  174.  For  Z  =  o,  and  later  for  Z  =  5,  7,  to  20  cm.,  no 
acoustic  pressures  (s  =  o)  were  obtainable.  On  either  side  of  l  =  3  cm.  the 


1 


graphs  therefore  fall  off  abruptly,  as  heretofore.  However  for  Z<  3  cm.  the 
graphs  were  found  still  to  rise,  showing  that  Z  =  3  is  not  as  favorable  an  adjust¬ 
ment  for  maximum  5,  as  it  was  in  figure  174. 

Briefly,  therefore,  the  acoustic  pressures  must  be  regarded  as  produced 
by  the  nodes  of  the  inner  quill  l';  but  this  is  ineffective,  except  in  the  presence 
of  short  critical  lengths  of  the  outer  quill,  Z.  Since  both  quill-tubes  are  clear, 
such  a  difference  of  behavior  may  be  associated  with  the  fact  that  l'  terminates 
in  the  closed  though  capacious  U-tube  reservoir,  whereas  Z ,  open  to  the  atmos¬ 
phere,  acts  by  virtue  of  its  node  like  a  valve. 

A  systematic  repetition  of  the  work,  given  in  part  in  figures  176  and  177 
and  the  summary  (fig.  178),  added  nothing  essentially  new.  The  curves  of 
figure  176  (l  —  1  cm.)  all  exhibit  crests  at  an  intermediate  pitch  C  =  0.7  mf. 
This  tendency  is  quite  lost  in  figure  177,  for  Z  =  2,  where  the  curves  are  accel¬ 
erated  and  possibly  even  intersect  on  the  left.  By  merely  changing  the 
insertion  of  the  outer  quill,  l  —  2  cm.,  it  was  possible  to  obtain  an  upper  curve 
as  high  as  5  =  85  at  C=  1.0;  on  the  other  hand,  by  adding  an  extension  of  but 
5  mm.,  the  Cs  curve  dropped  almost  to  zero  throughout — all  of  which  shows 


PROBE  AND  THE  INTERFEROMETER  U-GAGE 


95 


the  capriciousness  of  the  present  group  of  experiments  with  clear  quill -tubes. 
At  Z  =  4  cm.,  the  curves  were  much  like  figure  177,  but  lower.  Here  at  Z'  =  14 
an  isolated  high  Cs  graph  was  obtained  in  the  first  experiments,  which  could 
not  be  reproduced  in  many  subsequent  trials.  This  suggests  that  with  extreme 
delicacy  of  length  (Z)  adjustment,  other  isolated  maxima  might  be  brought 
out.  At  Z  =  6  cm.  or  larger,  the  Cs  graphs  were  at  5  =  o  throughout. 

Figure  178  gives  the  acoustic  pressures  corresponding  to  the  different 
outer  quill-tube  lengths,  Z  =  1,  2,  3,  4,  6  cm.,  in  their  dependence  on  the  inner 
quill-tube  lengths,  l'.  It  is  a  curious  collection  of  apparently  unrelated  graphs. 
Figure  177  shows,  however,  that  at  a  lower  pitch  (the  equivalents  of  C  >  1 . 1 
microfarads) ,  longer  outer  quills  than  Z  =  4  would  be  available ;  for  below  C  —  0.5 
microfarad  almost  no  acoustic  pressure  is  ever  appreciable,  whereas  above 
C=i.o  microfarad  all  the  graphs  (even  when  Z  =  6  cm.)  show  a  tendency  to 
rise.  The  chief  crests  fall  in  their  V  position  as  Z  increases  from  Z  =  2  cm.  Thus 
Z+T  =  2  +  22,  3  +  14,  (3)4-10,  44-6,  64-0  at  the  crests. 

The  puzzling  feature  of  figure  178  is  thus  the  short  range  of  lengths 
(Z  =  1  ....  4  cm.)  which  is  admissible  in  the  outer  quill-tubes,  if  acoustic 
pressures  5  are  to  be  obtainable.  Meanwhile,  the  inner  quill  Z'  admits  of 
relatively  very  large  elongation.  Except  perhaps  for  Z  =  1  cm.,  high  C  values, 
or  low  pitch  is  favorable  to  acoustic  pressure.  Hence  all  details  relative  to 
the  insertion,  etc.,  of  the  Z  quills  become  of  critical  importance  and  the  ob¬ 
served  variations  of  5  are  liable  to  be  capricious  over  wide  ranges  of  5.  With 
long,  wide  tubes  attached  at  Z  no  acoustic  pressures  were  obtainable. 

Negative  5  to  the  extent  of  a  few  fringes  was  occasionally  recorded.  In 
one  instance  a  short  end  of  thin  rubber  tubing  (2.7  cm.  long,  5  mm.  in  bore) 
inserted  at  Z  gave  5=10  of  negative  acoustic  pressure  consistently.  Such  a 
result  is  hard  to  explain.  On  constricting  the  outer  end  of  the  rubber  pipe 
enormous  positive  pin-hole  effects  were  of  course  obtained.  Thus  there  may 
have  been  a  slight  constriction  of  the  inner  end  of  the  rubber  tube,  producing 
the  reentrant  effect;  but  this  is  not  probable. 

61.  Reversal  of  the  preceding  adjustment — After  finishing  the  work  of 
the  last  paragraph,  a  large  number  of  isolated  experiments  were  made  with  a 
further  bearing  on  the  phenomena.  Taking  the  favorable  length  lf  =  20  cm. 
and  slightly  varying  the  Z  =  2  cm.  (very  nearly),  it  was  found  that  acoustic 
pressure  could  be  increased  to  even  5  =  120  in  the  given  scale  with  a  quill- 
tube  3  mm.  in  bore.  On  replacing  the  outer  quill  to  1  =  1.8  cm.,  the  pressure 
fell  to  5  =  60,  showing  that  the  adjustment  at  Z  must  be  accurate  to  fractions 
of  a  millimeter.  Furthermore,  on  increasing  the  bore  d  of  the  tube  Z  =  2  cm. 
to  d  =  5  mm.,  acoustic  pressure  practically  vanished.  Reducing  the  bore  to 
1  mm.  (retaining  1  =  2  cm.),  5  =  20  was  observed;  while  for  a  length  of  Z  =  1  cm. 
of  this  i-mm.  tube,  5  =  45  resulted.  Hence  the  bore  is  equally  important,  as  if 
a  critical  frictional  resistance  were  in  question. 


96 


ACOUSTIC  EXPERIMENTS  WITH  THE  PIN-HOLE 


The  inner  quill-tube,  l',  is  less  exacting.  Replacing  it  by  ends  of  rubber 
hose,  4  to  5  mm.  in  bore,  I  obtained  (1  =  2  cm.,  bore  3  mm.) 

/'  =  16  18  22  25  cm. 

j  =80  90  no  100 

the  favorable  case  just  cited. 

The  desirability  of  inverting  the  character  of  the  preceding  experiments, 
by  using  the  shortest  possible  /'  pipe  (junction  of  the  tt'  pipe  with  the  U-gage 
reservoir)  and  elongating  the  l  quills,  presented  itself.  Would  the  results  in  s 
be  symmetrical  and  acoustic  dilatations  result  from  such  a  reversal?  This 
was  pronouncedly  not  the  case.  In  fact,  the  apparatus  now  was  relatively 
inert. 

Tests  made  for  V  =  3  cm.,  bore  3  mm.  (smallest  available),  and  l  increasing 
from  1  to  50  cm.,  as  a  rule,  gave  no  response  in  5,  except  at  certain  definite 


lengths,  when  the  long  quill  sounded  a  high  overtone  of  the  deep  telephone- 
note.  Thus  I  recorded  ((7=1.0  mf.) 

V  =  3  cm. 

1=2  o  40  50  60 

*=  5  i5(<*"?)  i7(/"?)  5 

A  number  of  trials  produced  nothing  better.  The  evidence,  therefore,  is 
definitely  always  a  pressure;  but  when  l  is  prolonged  for  a  small  the  maxi¬ 
mum  5  is  not  more  than  20  per  cent  of  the  s  value  produced  with  long  l'  by 
the  short  l  pipe  in  the  preceding  paragraph.  There  the  l  pipe  node,  under  con¬ 
ditions  of  resonant  vibration,  acted  like  a  valve  to  increase  the  acoustic  pres¬ 
sure  in  tt',  which  in  turn  was  further  amplified  by  the  l'  pipe  nodes. 

The  most  hopeful  way  of  furthering  the  present  inquiry  seemed  to  consist 
in  balancing  the  U -reservoir  on  one  side  of  tt'  by  a  bulb  B  (fig.  179)  about  6 
cm.  in  diameter,  with  two  necks  l,  l".  The  quill-tube,  l  =  3  cm.  long,  was  used 
as  a  junction.  Here  the  bulb  alone  with  the  neck  at  l"  about  5  mm.  in  diam¬ 
eter,  1  cm.  long,  gave  the  small  but  definite  negative  reaction  shown  in  figure 
1 80a.  Inserting  the  quill-tubes  at  l",  the  curves  b  were  obtained,  practically 
coincident  for  all  lengths,  l"  =  2  to  28  cm.  The  graph  represents  only  about 
half  of  the  acoustic  pressure  obtainable  from  1  =  2  cm.,  alone. 

The  effect  of  the  l"  length  is  thus  nearly  negligible.  Not  so,  however, 
the  l  length  at  the  junction.  Figure  181  shows  that  for  1  =  3  cm.  there  is  a 


PROBE  AND  THE  INTERFEROMETER  U-GAGE 


97 


distinct  maximum  rise  of  the  Cs  graph;  for  l  =  2  it  is  much  lower  and  for  l  =  4, 
6,  8  cm.,  etc.,  lower  still  and  just  noticeable.  Here  again,  therefore,  the 
critical  tuning  conditions  are  associated  with  l  and  the  bulb  has  merely 
changed  the  favorable  length  from  1  =  2  to  /  =  3  cm.  Compared  even  with 
figure  177  the  pressures  are  low. 

62.  Quill-tubes  of  constant  external  diameter,  reduced  in  length  and  bore 
conjointly — We  finally  come  to  a  probable  solution  of  the  preceding  intricacies. 
Quill-tubes,  inserted  coaxially  with  short  pieces  of  rubber  tubing,  are  neces¬ 
sarily  shouldered  at  one  end  (insert  a,  fig.  182).  The  quill-tube  q  thus  effects 
a  reduction  of  the  diameter  of  the  anterior  tubulure  p  and  may  therefore  in  a 
measure  take  the  place  of  a  pin-hole.  To  test  this  surmise,  tubes  of  the  same 
diameter,  but  of  small  bore,  the  length  of  which  is  successively  diminished, 
may  be  taken.  The  adjustment  is  shown  in  figure  1826,  where  /  is  the 
length  of  small-bore  tube  inserted  in  the  wider  quill  q.  As  before,  tt'  is  the  tele¬ 
phone-pipe  with  the  quill-tube  V  (here  27  cm.  long  for  convenience),  joining 
tt'  with  the  U-gage.  The  Cs  graph  for  the  former  quill-tube  (1  =  2  cm.,  diam¬ 
eter,  d  =  0.3  cm.)  is  repeated  from  the  preceding  experiments  for  comparison. 

The  other  graphs  of  figure  182  refer  to  the  small-bore  tubes  d  =  0.2  cm. 
in  diameter  and  respectively  1  =  2,  1,  0.5  cm.  in  length,  in  question.  In  the 
former  case  they  are  inserted  saliently;  in  the  latter  (Z  =  o.5  cm.)  the  insertion 
may  easily  be  made  at  the  rear  (reentrant)  or  at  the  front  end  (salient)  of  a 
short  piece  of  slender  rubber  tubing  (2  cm.  long,  0.5  cm.  diameter),  acting  as  a 
quill-stem. 

When  l  =  2  cm.  the  graph  is  slightly  negative.  When  l  =  1  cm.  the  saliency 
of  the  insertion  is  manifested,  as  s  is  positive  within  the  limits  of  C.  By  a 
different  insertion  of  l ,  this  graph  could  have  been  made  negative.  When 
/  =  0.5  cm.  we  have  an  approach  to  a  coarse  pin-hole.  Placed  in  the  outer  end 
of  the  rubber  junction  with  tt,  the  corresponding  graph  is  strongly  positive. 
Placed  at  the  inner  end  of  the  junction  with  tt',  the  graph  soon  becomes 
strongly  negative,  though  it  is  a  complicated  graph  with  double  inflections. 
There  is  in  such  a  case  both  an  anterior  and  a  posterior  wider  quill-end, 
perhaps,  and  a  better  mode  of  insertion  must  be  devised.  At  all  events,  the 
short  capillary  tube  with  rubber  prolongation  now  acts  like  a  pin-hole  probe 
with  a  node  on  the  inside  of  the  rubber  quill,  at  the  constricting  hole,  and  in  a 
position  where  a  maximum  of  vorticity  may  be  expected.  The  Cs  graphs 
change  sign  on  reversal. 

In  figure  183  (in  which  the  results  as  a  whole  are  more  negative  than 
figure  182),  the  experiments  were  repeated  with  the  attached  bulb  B  (see 
inserts).  The  graph,  1  =  2,  d  =  0.3  cm.,  is  supplied  for  reference.  The  case 
1  =  2,  d  =  0.2,  is  much  like  the  preceding,  without  the  bulb.  So  is  graph  for 
l  =  i,  d  =  0.2  cm.,  though  here  there  is  a  remarkable  shoulder  to  the  graph  at 
C  =  0.9  microfarad,  after  which  there  is  an  almost  sheer  descent  toward  nega¬ 
tive  values.  The  case  1  =  0.5,  d  =  0.2  cm.  has  again  been  worked  out  both  for 
salient  and  reentrant  adjustments,  as  shown  by  the  inserts.  The  same  con- 


98 


ACOUSTIC  EXPERIMENTS  WITH  THE  PIN-HOLE 


elusions  may  be  drawn  as  before.  The  bulb  effect  is  a  depression  into  negative 
values. 

The  hump  of  the  curve  /  =  i,  d  =  0.2  cm.  deserves  further  mention.  Since 
the  constriction  l  is  in  the  main  reentrant  in  relation  to  the  bulb  B,  it  is  prob¬ 
able  that  as  pitch  descends  ( C  increasing),  the  resonance  note  of  B  is  being 
approached.  When  it  is  reached  beyond  the  limits  of  the  figure,  the  curve 
should  pass  through  a  negative  trough  at  the  resonance  pitch  of  B.  Similarly 
the  reentrant  graph  1  =  0.5,  d  —  0.2  shows  accelerated  fall  after  C  =  0.9  micro¬ 
farad.  All  the  curves  instance  the  desirability  of  higher  C  values  (lower  pitch). 

It  is  now  clear  that  if  the  work  of  figures  182  and  183  were  continued,  by 
further  reducing  both  l  and  d  conjointly,  the  relatively  enormous  full  pin-hole 
effect  in  s  would  ultimately  be  reached,  without  any  need  of  slope  in  the  walls 


of  the  pin-hole.  Whether  this  is  conical  or  not  seems  thus  to  be  without  con¬ 
sequence.  A  node  at  the  pin-hole  inside  the  quill-tube,  the  latter  functioning 
like  a  closed  organ-pipe,  is  accountable  for  the  acoustic  pressure  s;  and  5 
increases  with  the  intensity  of  the  node,  i.  e.,  with  the  increased  perfection 
in  the  tuning  of  the  probe  relatively  to  the  acoustic  pipes,  like  tt'.  The  node 
carries  the  excess  mean  pressure  over  atmospheric  pressure.  The  stream¬ 
lines  run  from  the  pin-hole  into  the  quill-tube  of  the  probe,  regarded  as  a 
closed  organ-pipe.  Hence,  if  the  pin-hole  node  is  within  the  acoustically 
vibrating  region  tt '  (organ-pipe  with  salient  pin-hole  probe)  there  is  acoustic 
pressure;  if  the  pin-hole  node  is  outside  of  the  region  tt'  (reentrant  pin-hole 
probe)  there  is  mean  dilation  in  tt'.  A  single  pin-hole  may  be  reenforced  by  a 
second  one  in  series  with  it,  between  tt'  and  the  U-gage.* 

The  reversed  experiment  was  equally  decisive.  Some  results  are  given  in 

*  A  supplementary  series  of  experiments  will  be  discussed  in  §  84  et  seq.,  particularly 
in  §  90. 


PROBE  AND  THE  INTERFEROMETER  U-GAGE 


99 


figures  184  and  185,  the  insert  in  the  latter  giving  the  adjustment.  The  inner 
quill  V  was  kept  1 5  cm.  in  length,  and  this  carries  the  cylindrical  constriction 
l"  (0.5  cm.  long,  bore  d  =  2  mm.),  immediately  adjoining  it The  outer  quill 
was  elongated  from  /  =  2  cm.  to  /  =  16  cm.  and  one  notes  a  marked  change  in 
the  form  of  the  Cs  graphs,  even  in  passing  from  /  =  2  to  l  =  4  cm.  Some  of  this 
is  referable  to  the  capricious  behavior  of  the  telephone-plate  in  its  supply  of 
overtones,  perhaps. 

As  it  takes  some  time  to  trace  any  one  of  the  Cs  graphs,  the  Is  graph  given 
in  figure  185  was  worked  out  directly  for  C=i.o  microfarad  and  /'  =  1 5  cm. 
The  strong  cusplike  maximum  for  1  =  2  cm.  is  here  again  encountered  (as  in 
fig.  178,  for  instance),  and  its  sharpness  shows  the  accuracy  of  tuning  the  l 


length,  required.  Beyond  the  diagram  (above  l  =16  cm.)  there  is  to  be 
another  but  flat  crest.  The  fall  to  and  rise  from  the  long  meandering  trough 
from  /  =  4  to  1=12  cm.  is  noteworthy. 

Thus  we  have  here  again  the  pin-hole  effect  on  a  small  scale,  which  could 
be  increased  by  simultaneously  decreasing  length  l"  and  diameter  d  of  the 
cylindrical  constriction  simulating  the  pin-hole  to  a  critical  value. 

The  consistent  results  thus  obtained  prove  that  a  strictly  cylindrical 
aperture  at  the  constriction  of  the  quill-tube  suffices  to  produce  the  pin-hole 
phenomena,  at  least  on  a  smaller  scale;  and  that  conical  walls  are  not  neces¬ 
sary.  One  suspects  that  the  abundant  production  of  vortices  on  the  inside 
of  the  probe  at  the  shoulder  (node)  of  the  constriction  is  the  ultimate  cause  of 
the  pin-hole  phenomena.  Such  ring  vortices,  whose  line  of  symmetry  coin¬ 
cides  with  the  axis  of  the  pin-hole,  would  produce  a  smaller  outflow  from  the 
pin-hole  probe,  as  compared  with  the  inflow  into  it  at  the  node.  In  other 


100 


ACOUSTIC  EXPERIMENTS  WITH  THE  PIN-HOLE 


words,  the  flow  excess  through  the  pin-hole  is  into  the  region  of  excess 
vorticity. 

At  the  same  time,  this  argument  loses  some  of  its  cogency  when  it  is 
recalled  that  the  node  in  the  pipe  tt'  (fig.  182),  which  reciprocates  with  the 
node  in  the  probe,  ql}  has  been  ignored.  Hence  in  paragraph  90,  identical 
quill-tubes,  on  opposed  sides  of  a  pin-hole  pricked  in  a  sliver  of  mica,  will  be 
examined.  It  will  be  found  that  even  such  an  ideally  thin  pin-hole  has 
opposed  properties  on  its  two  sides,  changing  +5  into  —s  on  reversal  of  the 
mica  plate. 

63.  Acoustic  pressures  in  case  of  a  soap-bubble — The  acoustic  pressures 
encountered  in  the  above  experiments  are  often  many  times  larger  than  the 
pressures  within  a  moderately  sized  soap-bubble.  One  might  infer,  therefore, 
that  such  a  bubble  could  actually  be  blown  with  the  telephonic  apparatus 
and  pin-hole  probe  described.  It  seemed  worth  while  to  try  this  with  an 
apparatus  sketched  in  figure  186,  where  TT  are  the  two  telephones  vibrating 
in  series  and  tt'  the  acoustic  pipe  joining  them.  At  5  is  the  salient  pin-hole. 
The  quill-tube  rU  connects  with  the  U-gage  for  registering  the  acoustic 
pressure.  A  T-branch  at  /  carries  a  small  funnel,  from  which  the  bubble  B 
may  be  blown  and  a  second  T-branch  at  e ,  with  a  stopcock,  may  be  used  for 
blowing  the  bubble;  but  it  is  usually  more  convenient  first  to  blow  the  bubble 
from  /  and  then  insert  it.  If  desirable,  a  second  pin-hole  may  be  used  at  r, 
in  series  with  5. 

If  the  bulb  B  is  rigid,  even  a  flask  of  one-half  liter  capacity,  the  acoustic 
pressure  at  U  appears  at  once,  and  in  these  experiments  was  about  5  =  250. 
With  an  appreciable  leak  in  the  flask  it  fell  immediately  to  zero.  Hence  the 
apparatus  itself  was  in  good  condition. 

Soap-bubbles  of  various  sizes  were  now  blown  and  attached  as  shown. 
In  every  case  the  pressure  fell  to  the  value  corresponding  to  the  radius  of  the 
bubble.  With  large  bubbles,  5  =  60,  with  smaller  ones  5  =  120,  with  flattish 
films  5  =  50,  for  instance,  were  recorded,  all  much  within  the  acoustic  pressure 
inside  a  rigid  system.  This  pressure  decreased  about  10  per  cent  when  the 
telephones  were  silenced  and  increased  again  when  they  sounded — a  result  to 
be  expected,  since  the  air  of  the  bubble  escapes  slowly  at  the  pin-hole  5,  in 
the  absence  of  acoustic  vibration.  For  the  same  reason,  5  slowly  increases  as 
the  bubble  contracts.  While  the  telephones  are  sounding,  however,  there  is 
no  escape  of  air  from  the  pin-hole  and  the  pressure  5  remains  constant  till  the 
bubble  bursts,  some  time  afterward. 

Thus,  to  develop  the  acoustic  pressure  in  full  requires  rigid  walls  through¬ 
out.  One  might  have  supposed  that  in  the  endeavor  to  reach  the  limit  of  this 
pressure  there  would  be  ingoing  current  at  5,  figure  186,  i.  e.,  continual  inflow 
of  air  in  the  direction  sr,  in  which  case  the  bubble  would  be  inflated  with 
continually  decreasing  interval  pressure;  but  this  is  not  the  case,  and  the 
acoustic  pressure  can  not  rise  above  the  resistance  corresponding  to  the 


PROBE  AND  THE  INTERFEROMETER  U-GAGE 


101 


elastic  walls  of  soap-film.  Current  at  5  inward  is  impossible,  though  any 
outward  flow  is  checked  when  acoustic  vibration  occurs. 

The  inversion  of  this  experiment  is  of  particular  interest.  The  adjustment 
is  sketched  in  the  insert  (fig.  187,  curve  d ).  The  bubble  B  with  its  funnel  / 
here  replaces  the  outer  quill-tube  l,  and  thus  the  bubble  contributes  an  incre¬ 
ment  to  the  atmospheric  pressure  in  t,  the  pipe  joining  the  telephones.  The 
pin-hole  probe  l  communicates  with  the  U-gage,  as  usual,  with  a  quill  17  cm. 
long. 

In  the  absence  of  the  bubble,  the  low  graph  187a  was  obtained.  The 
small  acoustic  pressures  here  are  the  result  of  the  necessarily  long  quill-tube 
connector  l  (12  cm.  long)  in  this  experiment;  for  with  the  2 -cm.  quill  the  graph 
takes  the  high  excursion  shown  at  h  in  figure  187.  It  does  not  differ  much 
from  the  graph  g,  obtained  in  the  former  experiment,  when  the  funnel  /, 
depending  from  is  closed  by  a  plug  of  liquid. 

Bubbles  were  now  blown  of  different  sizes  and  attached  at  l.  Examples 
of  the  results  are  recorded  by  the  graphs  b ,  cy  d ,  e ,  in  the  first  two  of  which 
the  bubble  burst  early.  Curves  d  and  e,  however,  were  carried  through 
without  mishap.  It  will  be  seen  that  these  graphs  are  exactly  like  graph  a  in 
shape,  throughout;  but  they  are  all  raised  to  different  high  5  values,  owing  to 
the  surface  tension  of  the  bubble  B  (see  insert)  attached  to  the  funnel  /. 

Thus  the  pin-hole  probe  l  builds  up  the  acoustic  pressure  in  the  gage  Ut 
from  whatever  pressure  it  finds  in  the  sounding-pipe  t,  provided  the  Ul 
system  is  rigid.  If  it  is  not,  the  limiting  pressure  of  the  elastic  walls  can  not 

be  exceeded.  The  graph  h  rises  so  rapidly  that  the  crests  in  a  b . e 

are  present,  if  at  all,  as  mere  sinuosities;  but  four  of  these  may  be  recognized, 
all  displaced  toward  lower  pitch  (larger  C  values)  as  compared  with  the 
a  ....  e  graphs. 


CHAPTER  IV 


PIPES  WITH  RELATIVELY  MASSIVE  AIR-COLUMNS.  ORGAN-PIPES. 

HORNS 

64.  Pin-hole  record  for  variable  organ-pipe.  Apparatus — The  closed 
organ-pipe,  p,  of  one-inch  brass  tubing,  shown  in  figure  188,  is  provided  with 
a  well-fitting  greased  plug,  a,  so  that  the  depth  d  may  be  varied  at  pleasure. 
The  pipe  is  blown  by  the  jet-pipe  /,  the  front  of  which  has  been  compressed 
wedge-shaped  to  a  narrow  cracklike  crevice,  through  which  a  thin  sheet  of 
air  is  forced.  This  air  lamella  is  cut  parallel  to  its  surface  by  the  thin  blade 
/,  sharpened  where  it  meets  the  air-current.  Moreover,  /  is  adjustable  on 
side-slides,  so  that  the  width  of  embouchure,  e ,  may  be  varied  to  get  the 
clearest  tone  in  any  case.  Finally  the  long,  slender  probe  be  (45  cm.  to 
U-tube)  is  inserted  out  of  the  way  of  the  air- jet  from  /,  so  that  the  pin-hole 
at  c  may  be  near  the  bottom  of  the  organ-pipe.  The  advantage  of  the  pipe 
is  its  loud  tone  and  the  fact  that  air  is  not  blown  into  the  pipe  at  the  embou¬ 
chure.  If  d  denotes  the  depth  of  the  plug  below  the  outlet,  clear  notes  were 
obtained  from  the  pipe  as  follows: 


d  =  .. . 

15 

14.5 

13.5 

12.5 

11. 5 

10.5 

9.5 

8.5 

7.5 

6-5 

5-5 

4.5 

3-5 

2.5 

1-5 

1.0 

0.5  cm. 

Note. 

c" 

%C" 

d" 

be" 

e" 

r 

g" 

a" 

b  b" 

c"’ 

d"' 

e'" 

r 

c/v 

e'v 

£/v 

cy 

only  the  last  being  conjectural.  As  it  was  found  that  a  steady  fringe  dis¬ 
placement,  5,  could  be  obtained,  the  pipe  in  the  first  experiments  was  blown 
by  the  mouth  of  the  observer. 

66.  Results — Experiments  with  air-blown  pipes  are  not  easily  put  under 
control,  and  the  individual  observations  are  liable  to  be  straggling.  Thus, 
the  intensity  of  the  note  depends  markedly  on  a  proper  spacing  of  the  em¬ 
bouchure  e ,  among  other  things.  In  figure  189,  in  which  this  intensity  or 
acoustic  pressure  5  is  expressed  in  terms  of  the  depth  d ,  of  the  plug  a ,  below 
the  mouth  of  the  pipe,  ef  was  set  for  the  strongest  note.  Circles  open  or 
closed  denote  different  series  of  observations,  be  remaining  constant  (45  cm.) 
in  length  and  the  pin-hole  c  at  the  bottom  near  a. 

On  starting,  there  is  a  low-pressure  hiss  before  the  pipe-note  breaks  forth. 
The  pressures  here  are  invariably  negative  (as  would  be  supposed)  and  of  the 
value  given  by  the  graph  marked  wheeze.  The  negative  pressures  may,  of 
course,  be  much  enhanced  if  for  any  reason  the  pipe  does  not  sound  while  the 
jet  velocity  is  increased.  This  was  also  often  the  case  when  the  very  high, 
shrill  harmonics  are  evoked  from  the  pipe.  In  general,  at  the  beginning,  the 
pressure  throughout  the  pipe  is  markedly  below  that  of  the  atmosphere. 
As  soon  as  the  pipe  strikes  its  note,  however,  there  is  a  definite  pressure,  s, 

102 


PIN-HOLE  PROBE  AND  THE  INTERFEROMETER  U-GAGE 


103 


usually  in  marked  degree,  positive  as  instanced  by  the  graph  figure  189. 
Though  drawn  through  straggling  data,  its  implications  are  clear  enough. 
If  the  pipe  is  shallow  (e"'—c"r),  acoustic  pressure  s  is  here  negative,  as  one 
should  expect  from  the  proximity  of  the  plug  a  to  the  embouchure,  among 
other  things.  Between  c"'  and  e",  however,  acoustic  pressures,  built  up  from 
the  initial  negative  pressure-level,  are  positive,  passing  through  a  maximum 
at  about  g",  d  =  10  cm.  For  the  deep  pipe,  between  be"  and  c"}  the  pressures 
are  negative  again,  and  there  is  a  pronounced  trough  at  about  d".  This 
would  not  have  been  expected.  The  wheeze  graph  seems  to  show  a  similar 
tendency  here  and  the  high  negative  values  are  further  enhanced  by  it. 

Since  the  endeavor  was 
made  to  keep  the  embouchure 
e  at  the  distance  of  maximum 
efficiency,  the  crests  and  troughs 
can  hardly  be  ascribed  to  it. 

Nor  would  this  account  for 
sinuosities  if  e  were  constant. 

There  would  be  a  mere  passage 
of  s  through  a  maximum. 

It  seems,  therefore,  that 
the  undulatory  results  obtained 
must  be  associated  with  the 
length  of  quill-tube  (45  cm.) 
carrying  the  pin-hole.  This  is 
in  accord  with  the  indications 
of  the  preceding  paragraphs. 

To  test  this  surmise,  the  quill- 
tube  was  elongated  10  cm. 

(*  =  55  cm.  in  length).  It  was 
now  found  that  at  ^  =  7.5  cm., 
the  small  5  deflections  of  figure 
189  could  easily  be  built  up  to  5  =  100  or  even  120,  whereas  with  #  =  45  cm. 
they  were  liable  to  be  small  or  negative. 

Though  this  result  seems  to  verify  this  surmise  here,  the  experiments  of 
the  next  paragraphs,  with  stronger  and  continued  air-currents,  are  quite 
out  of  keeping  with  it;  for  connectors  between  pin-hole  probe  and  U-tube  of 
any  length  (even  10  feet)  made  very  little  difference  in  the  results.  It  is  not, 
therefore,  opportune  to  conjecture  further  explanations  of  these  very  com¬ 
plicated  phenomena  until  additional  experiments  with  organ-pipes  blown  by 
more  steady  and  persistent  air-pressures  are  at  hand. 

66.  Further  experiments — For  the  new  experiments,  a  large  Fletcher 
bellows  actuated  by  an  electric  motor  was  installed.  The  pin-hole  of  the 
preceding  experiments  (punctured  in  thin  metal  plate)  was  replaced  by  a 
glass  cone  pin-hole.  The  latter  (shown  at  g  in  figure  190,  where  p  is  the 
8 


104 


ACOUSTIC  EXPERIMENTS  WITH  THE  PIN-HOLE 


organ-pipe  blown  by  the  jet  /,  and  adjustable  blade  /)  was  now  mounted  in 
the  plug  a,  the  pin-hole  being  flush  with  the  bottom  of  p  and  displaced  with 
it.  A  wide  stem,  be,  0.6  cm.  in  diameter  and  16  cm.  long,  was  needed  to 
receive  the  glass  quill-tube  g,  properly  sealed  in.  The  end  b  was  then  joined 
to  the  U-tube  by  rubber  tubing,  the  length  of  which  was  here  of  little  con¬ 
sequence.  A  long  connector  was  therefore  preferred,  as  it  kept  the  vibrations 
of  the  acoustic  installment  from  shaking  the  interferometer  U-tube.  With 
an  air-pressure  as  furnished  by  the  bellows  (not  quite  steady),  the  fringes 
oscillated  between  limits  reaching  their  largest  displacement  when  the  air- 
current  was  smallest.  The  overblown  pipe,  therefore,  loses  acoustic  efficiency 
for  the  given  embouchure.  The  Fletcher  bellows  was  chosen  here  because 
its  mean  pressure  is  constant,  and  it  has  the  great  advantage  of  starting  the 
pipe-note  with  an  initial  puff,  as  it  were,  more  easily  than  a  steady  blast. 


Figure  19 1  (curves  a  and  b)  gives  the  results  of  the  acoustic  pressure  h 
in  centimeters  of  mercury,  observed  at  the  bottom  of  the  pipe  p ,  when  the 
depth  d  varies.  The  jet  pressure  in  curve  a  was  somewhat  above  that  in 
curve  b,  the  embouchures  being  adjusted  accordingly.  These  two  graphs 
differ  not  only  in  appearance  from  the  preceding  graph,  figure  189,  but  the 
acoustic  pressures  represented  are  much  larger.  For  if  A r  be  the  micrometer 
displacement  corresponding  to  A h  (mercury  head),  Ah  —  o.jiAr  at  an  incidence 
of  450,  while  a  direct  standardization  of  the  ocular  scale-parts  s,  showed 

iooAs  =  io.8Ar 

in  scale-parts,  each  of  the  latter  being  io"3  cm.  Thus,  for  the  same  A r, 

Ah/As  =  0.71/0. 108  =  6.6 

Hence  the  unit  of  the  scale  of  figure  19 1  is  6.6  times  that  of  figure  189.  More- 


PROBE  AND  THE  INTERFEROMETER  U-GAGE 


105 


over,  the  ocular  scale-part  5  corresponds  to  o.io8Xio-3Xo.7i  =  76.7Xio~6 
cm.  Hg.  or  about  the  millionth  of  an  atmosphere;  that  is,  roughly,  dynes/cm2. 

For  convenience,  the  graph,  figure  189,  reduced  to  the  same  scale  as  figure 
19 1,  has  also  been  inscribed  in  that  figure. 

If  we  compare  figure  189  for  relatively  low  jet-pressure,  with  figure  19 1, 
curve  a,  for  high  jet-pressure,  we  notice  that  the  crests  or  optima  of  the 
graphs  fall  somewhere  between  the  depths  d  =  8  and  d  =  10  cm.,  in  both  cases. 
The  pipe  responds  best  for  notes  between  g"  and  b",  though  the  crest  of  the 
curve  b  for  somewhat  lower  jet-pressures  is  smaller  in  depth,  d.  The  differ¬ 
ence  between  the  curves  is  the  much  greater  breadth  in  pitch  of  the  graph, 
figure  19 1,  for  positive  h.  In  the  latter  curves  negative  acoustic  pressures  do 
not  appear,  so  far  as  tests  of  the  crest  is  reached,  and  below  the  crest,  not 
until  the  pitch  is  below  cv ,  or  d  <  2  cm.  in  pipe-depth.  Remembering  that 
irregularities  due  to  the  set  of  the  embouchure  are  inevitable,  the  relation  is 
almost  as  if  the  curve  a  were  dropped  in  a  vertical  direction,  until  the  crests 
coincide,  except  that  the  development  of  negative  pressures  (s)  for  such  a 
case  does  not  appear.  It  is  particularly  noticeable  that  the  trough  above 
d— 12  cm.  (near  d")  is  suggested  in  all  cases. 

The  reason  for  an  optimum  of  the  pipe  for  pitches  between  a"  and  g" 
is  not  easily  conjectured,  because  outside  influence  due  to  pin-hole  and  its 
connection  with  the  U-tube  enter  into  the  consideration;  but  it  seems  to  me 
probable  that  the  optimum  is  a  property  of  the  organ-pipe  itself  and  referable 
to  the  embouchure  device.  One  notices,  for  instance,  that  at  any  fixed  pitch 
(or  depth  d  of  pipe),  the  maximum  fringe  displacement  is  gradually  reached 
within  the  lapse  of  seconds.  Energy  is  thus  being  continually  supplied  to  the 
acoustic  vibrations,  with  the  effect  of  gradually  increasing  its  amplitude  to  a 
limit.  This  energy  can  only  be  withdrawn  from  the  wheeze  or  siffle  at  the 
thin  edge  /  of  the  embouchure ;  and  one  concludes  that  a  mean  pitch  of  wheeze 
notes  is  most  efficiently  present,  in  correspondence  with  the  optimum  or 
crest-pitch  of  the  organ-pipe  itself. 

Another  conjectural  reason  for  the  graph,  figure  19 1,  may  be  sought  in 
the  possible  loss  of  the  efficiency  of  the  pin-hole  at  different  pitches.  Fre¬ 
quencies  larger  than  c'v  may  very  well  need  a  different  size  of  pin-hole  to  give 
positive  displacements  5  than  smaller  frequencies  and  a  particular  optimum 
frequency  corresponding  to  size  of  hole  would  be  expected.  Similarly,  the 
pin-hole  in  copper  foil  (fig.  189)  may  behave  differently  from  the  pin-hole 
in  glass  at  the  same  pitch,  in  relation  to  positive  and  negative  acoustic  pres¬ 
sures.  It  was  found,  however,  that  the  pin-hole  responds  to  shrill  overtones 
with  undiminished  strength,  so  that  the  behavior  of  the  pin-hole  is  probably 
not  in  question  here. 

67.  Reduced  diameter  of  pin-hole  probe  connector — It  has  been  stated 
that  the  length  of  the  tube  cb  between  pin-hole  g  (fig.  190)  and  U-gage 
seemed  to  make  little  difference  here.  The  question  thus  arises  whether  a 
reduced  caliber  of  the  stem  be  would  have  any  marked  effect,  such  as  one 


106 


ACOUSTIC  EXPERIMENTS  WITH  THE  PIN-HOLE 


should  expect  if  the  pin-hole  probe,  in  accordance  with  the  above  investiga¬ 
tions,  behaves  like  a  slender  organ-pipe  with  a  pin-hole  embouchure.  Ac¬ 
cordingly  the  stem  be  was  variously  constricted  with  capillary  tubes,  cotton 
inclosures,  etc.,  such  as  might  be  supposed  to  dampen  vibration  and  render 
the  pin-hole  probe  ineffective.  To  my  surprise,  these  insertions  had  but  a 
relatively  small,  if  any,  effect  in  the  large  number  of  special  tests  at  a  given 
pitch,  made  in  succession.  If  the  bore  is  too  small,  the  fringes  eventually 
drift,  owing  to  the  viscosity  of  the  air  passing  the  capillary  tube.  These 
questions  will  be  resumed  in  paragraph  69. 

In  figure  192  (also  inserted  in  fig.  191  for  comparison),  I  have  given  a 
complete  set  of  data  made  with  the  same  glass  pin-hole  when  the  capillary 
stem  (be,  fig.  190)  13  cm.  long  was  but  0.08  cm.  in  inside  diameter.  The 
optimum  depth  is  here  at  d  =  7  cm.  (somewhat  smaller  than  in  fig.  191)  and 
the  reduction  of  intensity  compared  with  curve  a  about  20  per  cent;  but  this 
is  to  be  ascribed  to  decreased  jet-pressure  or  velocity.  The  intersection  of  the 
graph  with  the  axis  (Ah  =  o)  is  the  same  as  before.  The  graph  from  here  rises 
almost  linearly  to  the  crest  and  thereafter  wavers,  falling  slowly.  The  trough 
above  d— 12,  however,  fails  to  appear.  Cutting  down  the  bore  of  capillary 
tube  further  by  inserting  a  wire  slightly  less  in  diameter  (0.06  cm.),  but  admit¬ 
ting  of  a  definite  fringe  displacement,  the  results  were  about  the  same.  It 
seems  impossible,  therefore,  that  in  so  fine  a  bore  anything  like  acoustic 
vibration  should  be  possible.  There  is  a  mere  conduction  of  static  pressure 
to  the  U-gage. 

The  data  of  figure  19 1  are  more  fully  recorded  in  the  following  table: 


Clear,  one- quarter  inch  connector 

d= . 

2 

3 

4 

5 

6 

7 

8 

9 

10 

11 

12 

13 

cm. 

AhXio3. . 

—2.1 

-0.7 

21.7 

34.1 

52.5 

49-7 

65.0 

67.7 

72.1 

69.6 

56.8 

65.5 

5i-5 

53-7 

67.0 

cm.  Hg. 

Same.  Smaller  pressures 

d= . 

2 

3 

4 

s 

6 

7 

8 

9 

10 

11 

12 

13 

cm. 

AhXio3. . 

—0.6 

“3-5 

132 

1 8.7 

37 

45 

43 

48 

62 

53 

55 

49 

34 

40 

34 

35 

•  • 

cm.  Hg. 

Capillary  connector,  bore  0.08  cm.,  length  13  cm. 

d  = . 

1 

2 

3 

4 

s 

6 

7 

8 

9 

cm. 

AhXio3 .. 

-1.9 

-5-5 

-.6 

8-5 

I9.I 

27.6 

36.2 

43.6 

38.5 

36.6 

cm.  Hg. 

d  -  •  •  •  •  •  • 

•  • 

95 

10.5 

ns 

12.5 

13.5 

14.5 

15  cm. 

AhXio3.. 

•  • 

•  • 

•  • 

•  • 

•  • 

37.2 

35-6 

36.6 

35-6 

35.9 

36.8 

36.4 

32.2 

3U5 

34-6 

33-8 

33-3 

29.5  cm.  Hg. 

l 


PROBE  AND  THE  INTERFEROMETER  U-GAGE 


107 


68.  Steady  blast — In  relation  to  figure  193,  the  pipe  was  blown  by  a 
steady  current  of  air  furnished  by  a  rotary  blower  controlled  by  a  motor. 
The  graphs  a,  b,  c  were  obtained  with  the  glass  pin-hole,  the  jet-pressure 
being  least  in  curve  a,  and  largest  in  curve  ct  with  b  intermediate,  so  far  as 
could  be  controlled.  The  ordinates  are  screw-micrometer  displacements  A r, 
at  the  depth  d  below  the  pipe-mouth,  and  we  have,  as  before,  Ah  =  0.71  A r  cm. 
of  mercury.  Again,  the  data  are  not  smooth,  owing  to  the  difficulty  in  obtaining 
the  best  set  for  the  blade  /  at  the  embouchure  e,  and  the  graphs  a,  b  have 
been  drawn  through  the  highest  points,  as  there  is  no  consistent  sinuosity. 
In  curve  c,  however,  where  a  larger  number  of  trial  settings  of  the  blade 
were  made  for  each  depth,  d,  to  obtain  the  best,  the  sinuous  character  of  the 


graph  could  not  be  eliminated.  The  optimum  in  cases  a  and  b  seems  to  be  at 
d— 10  cm.,  but  in  case  c  it  would  be  somewhat  higher.  The  curves,  moreover, 
cross  the  axis  (Ar  =  o)  at  d  —  1,  2,  4  cm.,  as  the  jet-pressure  or  velocity  dimin¬ 
ishes.  At  low  pressures  the  high  notes  often  fail  to  respond;  but  this  result 
may  be  secured  by  placing  the  hand  or  any  reflecting  object  at  the  proper 
distance  from  the  pipe-mouth.  The  note  is  then  stimulated  by  its  echo. 
In  fact,  the  fringe  displacement  (5)  will  rise  and  fall  as  the  reflecting  object 
is  moved  nearer  or  farther  from  the  mouth.  Another  interesting  feature 
is  the  growth  of  the  5  value,  here  again  appreciably  within  a  minute  or  more. 
Energy  is  very  gradually  being  absorbed  by  the  vibration.  Care  must  of 
course  be  taken  to  keep  the  jet-slit  clean. 

The  graphs  d  and  e ,  figure  193,  were  obtained  with  the  pin-hole  in  copper 
foil,  less  sensitive  than  the  glass  pin-hole.  The  jet-velocity  in  case  d  is  the 


108 


ACOUSTIC  EXPERIMENTS  WITH  THE  PIN-HOLE 


higher,  e  being  very  low.  I  expected  in  this  case  to  reproduce  the  negative 
pressures  (— Ar)  of  figure  189,  but  these  were  not  obtainable.  The  curves 
d  and  e  are  particularly  interesting,  because  the  sinuosities  seem  evidently 
to  correspond  almost  throughout.  This  is  the  first  case  of  a  consistent  result 
of  this  kind;  but  it  follows,  nevertheless,  that  the  sinuosities  may  be  more 
than  an  incidental  part  of  the  phenomena  and  not  merely  due,  for  instance, 
to  some  maladjustment  in  the  set  of  the  embouchure  blade.  In  fact,  the 
deep  trough  between  d  =  12  and  1 4  cm.  is  also  present  in  figure  189.  The  question 

thus  arises,  to  what  are  they  to 
be  referred.  It  is  again  suggested 
that  the  troughs  may  represent 
harmonics  unfavorable  to  the 
quill-tube  of  the  pin-hole  probe; 
for  without  being  the  cause  of 
the  main  phenomenon  of  acoustic 
pressure,  the  pin-hole  quill-tube 
may  nevertheless  modify  it  by 
periodic  increments,  if  the  tube 
(as  was  the  case  in  fig.  193,  d}  e ) 
is  clear. 

The  slow  growth  of  the  full 
amplitude  was  again  very  marked 
in  cases  d  and  e.  The  high-fre¬ 
quency  intensity  is  weak,  because 
this  would  need  an  accentuated 
jet-velocity  as  the  pitch  increases. 
Thus,  if  the  jet  is  stopped,  the 
opening  puff  is  intense. 

From  the  graphs  d  and  e  an  approximate  location  of  the  maxima  would 

place  them  as  follows: 

Maxima . cm  e"  f" 

d= . 15  11  9  6  4  cm. 

so  that  the  depths  are  nearly  as  5,  4,  3,  2,  1.  The  minima  lie  at 

Minima . b  b"  #/"  d" 

d= .  5  7-5  10  13 


these  being  the  organ-pipe  notes  to  which  the  quill-tube  does  not  easily 
respond.  They  lie  in  their  d  values,  almost  exactly  between  the  maxima. 

These  interesting  relations  suggest  a  final  experiment  of  direct  comparison 
of  the  empty  and  nearly  choked  quill-tube  (45  cm.  long)  as  to  acoustic  pres¬ 
sure,  Ar,  generated  under  otherwise  like  conditions.  The  inside  diameter  of 
the  quill-tube  was  0.230  cm.  It  was  closed  at  the  pipe-end  with  a  pin-hole 
foil.  To  nearly  choke  it,  a  cotton-covered  straight  copper  wire  0.19  cm.  in 
diameter  was  inserted,  running  from  end  to  end.  This  leaves  a  free  shell 
space  of  but  0.02  cm.  thick  between  wire  and  glass,  and  the  air  resistance 
introduced  was  such  that  at  least  1  minute  was  needed  to  obtain  the  maximum 


PROBE  AND  THE  INTERFEROMETER  U-GAGE 


109 


fringe  displacement,  at  any  pitch.  It  seems  impossible  that  acoustic  vibra¬ 
tion  could  occur  within  the  long,  rough  shell  in  question.  The  Fletcher 
bellows  was  used  to  actuate  the  jet  of  the  organ-pipe,  because  of  the  fixed 
mean  pressure  to  be  obtained  at  a  relatively  high  value. 

The  results  are  given  in  figure  194,  curve  g.  They  are  a  pronounced 
corroboration  of  the  curves  d,  e,  and  prove  that  the  decadence  of  the  latter 
graph  in  high  pitch  is  the  result  of  falling  jet-pressure.  There  are  the  same 
crests  and  troughs  in  all  curves;  in  curve  g,  however,  the  chief  maxima  are 
nearly  of  the  same  height. 

The  corresponding  results,  when  the  same  quill-tube  probe  was  all  but 
closed  from  end  to  end  by  the  copper  wire  in  question,  are  given  in  the  graphs 
/,  there  being  two  different  series  along  the  main  branch.  This  curve  is 
quite  different  from  curve  g.  The  marked  oscillation  of  the  latter  has  largely 
been  eliminated  and  /  is  more  like  the  preceding  graphs  with  glass  pin-holes 
and  wide  connector-tubes.  In  other  words,  the  tendency  of  /  is  to  run  along 
the  troughs  of  g,  as  if  the  oscillation  effect  of  the  clear  quill-tube  were  super¬ 
imposed  on  the  acoustic  pressure  independent  of  it. 

We  may,  therefore,  come  to  the  conclusion  that  the  acoustic  pressure 
at  the  base  of  the  closed  organ-pipe  may  be  conveyed  as  static  pressure 
to  the  U-gage.  This  pressure  may  be  periodically  (with  pitch)  enhanced 
if  there  is  oscillation  in  the  quill-tube  as  well.  In  the  case  of  wide  connector- 
tubes  (one-quarter  inch)  the  pin-hole  embouchure  is  probably  unable  to  stimu¬ 
late  appreciable  vibration  in  the  connector  and  the  acoustic  pressures  obtained 
are  without  the  systematic  undulatory  character.  Hence  such  tubes,  whether 
clear  or  partially  choked  from  end  to  end,  register  about  the  same  pressure. 

69.  Miscellaneous  tests — If  the  high-pitch  note  is  produced  not  as  a 
fundamental,  but  as  an  overtone  with  very  high  jet-velocity,  the  intensity  is 
indefinitely  high.  In  fact,  the  conditions  of  the  graphs,  figure  193,  may  be 
reversed.  Thus  for  a  mean  pipe-depth  and  fast  jet,  the  high  fifth  overtone 
was  of  intensity  Ah  =  116X0.71  Xio_3  =  io~3X82  cm.  of  Hg.  (narrow  spacing 
of  blade),  while  for  a  wider  spacing  the  fundamental  began  with  an  intensity 
of  but  Ah  —  yX  io~3  and  regularly  increased,  for  a  gradually  decreasing  jet- 
velocity,  ultimately  to  Ah  =  56  X  io~3  cm.  Hg.  Here,  therefore,  graphs  descend¬ 
ing  from  left  to  right  would  have  been  obtained,  had  it  been  possible  to  main¬ 
tain  the  high  jet-velocity. 

With  the  connector-pipe  be,  figure  193  (inset),  nearly  choked  with  cotton, 
but  still  admitting  of  a  slow  current  of  air  through  it,  conditions  under  which 
acoustic  vibration  would  hardly  seem  possible,  the  following  intensities  A r 
were  successively  found  with  a  gradually  decreasing  jet- velocity,  unfor¬ 
tunately  : 

Cotton  in . io3Ar. ...  93  . .  75  cm. 

Clear  tube,  be:  io3A r .  .90  . .  78  . .  cm. 

Thus  the  connector-pipe  be,  all  but  choked  with  cotton,  is  just  as  efficient 
as  the  clear  pipe,  so  that  conveyance  of  pressure  to  the  U-gage  seems  alone 


110 


ACOUSTIC  EXPERIMENTS  WITH  THE  PIN-HOLE 


to  be  in  question.  A  similar  experiment  in  which  a  capillary  tube  0.08  cm. 
in  bore  was  inserted  into  be  gave  alternately: 

Cap.  tube  in:  io3Ar . 104  .  59  . cm. 

Cap.  tube  out:  io3Ar .  80.  . . .  . .  42  cm. 

showing  that  fall  of  jet-pressure  is  alone  in  question.  Finally,  a  thermometer 
capillary  with  a  bore  of  but  0.03  cm.  and  length  16  cm.,  and  requiring  several 
minutes  to  reach  the  maximum  at  the  U-gage  gave: 

Cap.  in:  io3Ar . 37  cm.  Cap.  out:  io3XAr  =  i7cm. 

the  fall  of  jet- velocity  in  the  long  interval  of  waiting  being  here  again  in 
evidence.  Thus  a  connector-tube  of  any  length,  or  even  a  capillary  tube 
of  bore  sufficient  to  admit  of  a  reasonable  flow  of  air  through  it,  functions 
equally  well  to  connect  the  pin-hole  probe  with  the  U-gage. 

70.  Mean  total  pressure  in  organ-pipe.  Soap  film — From  what  has  pre¬ 
ceded  it  is  obvious  that  when  the  above  pipe  ( p ,  fig.  195)  is  not  sounding, 


the  pressure  within  must  be  negative.  The  graphs  for  d  =  o  cm.  give  a  value 
not  larger  than  io3Ar=io  cm.,  or  A/z  =  7Xio-3  cm.  of  mercury,  i.e.,  gXio~5 
atm.  below  the  pressure  of  the  atmosphere.  The  usual  jet-velocity  used  is 
here  understood. 

It  remains  to  determine  whether  the  mean  pressure  at  the  node  varies 
from  this  negative  datum  (caet.  par.)  when  the  pipe  is  sounding.  In  other 
words,  does  the  excess  pressure  within  the  rigid  boundary  of  pin-hole  probe 
and  U-tube  also  occur  at  the  organ-pipe  node  on  the  outside  of  the  pin-hole; 
or,  has  the  whole  vibrating  air-column  within  the  above  pipe  the  same  mean 
negative  pressure? 

To  answer  this  expeditiously,  I  adjusted  a  soap-film  c,  figure  195,  in 
the  thistle-tube  /  communicating  with  the  organ-pipe  p  through  the  perforated 
cork  a  at  the  bottom.  The  film  dipped  at  the  flare  of  the  thistle-tube  retreats 
to  the  position  c ,  where  it  is  in  stable  equilibrium  at  a  diameter  of  2.3  cm. 
On  sounding  the  pipe  the  effect  is  always  to  bulge  the  film  upward  as  at  b , 
showing  that  /  is  below  atmospheric  pressure.  If  the  note  is  too  intense,  or  if 
the  blade  /  at  the  embouchure  is  withdrawn,  the  film  may  break  loose  from 
its  position  c  and  move  upward  into  /  against  the  resistance  arising  from  its 
surface-tension,  T.  But  for  the  usual  strength  of  notes  used,  the  bulge  b 
was  about  0.5  cm.  high.  This  implies  a  soap-bubble  R— 1.2  cm.  in  radius. 


PROBE  AND  THE  INTERFEROMETER  U-GAGE 


111 


The  excess  pressure  within  such  a  bubble  would  be  £  =  2  T/R  dynes/cm2. 
If  T  —  50  dynes/cm.  for  the  soap-film,  £=100/1.2  dynes/cm.  2,  or  8.5X10  s 
atm.,  or  6.5  Xio"3  cm.  of  mercury.  This,  therefore,  is  the  pressure  deficiency 
at  the  node  within  the  organ-pipe  resulting  from  the  jet  velocity  at  the  em¬ 
bouchure;  and  it  is  the  same  order  of  value  obtained  with  the  pin-hole  probe 
and  U-tube  above. 

Thus  it  follows  that  the  mean  pressure  within  the  organ-pipe  is  the  same 
throughout  and  may  be  either  incremented  or  decremented,  depending  on  the 
way  in  which  the  pipe  is  blown  (jet  /).  The  positive  pressure  excess  regis¬ 
tered  by  the  pin-hole  probe  at  a  node  and  which  may  mount  even  to  1  mm.  of 
mercury  for  intense  notes  exists  only  within  the  pin-hole  probe  and  its 
rigid  accessories,  the  connector  pipe  and  U-tube.  If  the  walls  are  not  effec¬ 
tively  rigid  (if  for  instance,  part  of  the  region  is  closed  by  a  soap-film)  the 
pressure  within  the  probe  also  can  not  exceed  that  of  the  film. 

The  importance  of  these  results  in  their  bearing  on  an  explanation  of 
the  probe  is  obvious. 

71.  The  same.  Direct  U-gage  measurement — As  the  bearing  of  this 
experiment  on  an  explanation  of  the  pin-hole  probe  is  important,  it  was 
corroborated  by  direct  tests.  For  this  purpose  the  funnel  /  (fig.  195)  was 
removed  and  replaced  by  a  quill-tube  connected  at  the  far  end  with  the 
U-gage.  The  results  are  given  in  figure  196,  being  fringe  displacements  5 
(negative  upward)  for  successive  pipe-depths  d.  These  data  are  necessarily 
very  fluctuating,  depending  on  the  position  of  the  plate  F  (fig.  195).  When 
this  closed  the  pipe,  the  displacement  5  was  least;  when  F  was  removed  (open, 
silent  pipe),  5  was  usually  greatest.  Some  of  the  notes  (for  instance,  at  d=  12 
cm.)  did  not  readily  strike  and  high  negative  pressure  is  recorded.  The  mean 
pressure  may  be  taken  as  —  5  =  100 ;  or,  if  a  scale-part  is  estimated  at  io-6  atm., 
—  £  =  100  Xio_6X  76  =0.0076  cm.  Hg,  with  a  range  from  0.003  to  0.011  about. 
All  of  this  corroborates  the  above  estimates  and  suggests  a  further  reason  for 
5-differences  when  the  position  of  the  plate  F  is  changed. 

72.  Apparatus.  Broad  horn  (190) — Hitherto  in  my  work  short  and 
slender  pipes  (5  to  10  cm.  long,  1  cm.  in  diameter)  were  used  in  connection 
with  the  telephones.  These,  as  it  were,  are  at  the  mercy  of  the  telephones. 
The  present  investigation  of  broad  and  long  pipes  contrasts  with  this  and 
leads  to  a  number  of  interesting  results  bearing  on  the  acoustic  pressure  (s) 
indicated  by  the  pin-hole  probe.  As  first  found,  the  phenomena  with  the 
conical  horn  were  so  much  simpler  than  the  complicated  graphs  for  the 
cylindrical  pipe  that  the  use  of  the  former  in  connection  with  measurements  of 
alternating  currents  seemed  promising.  Later  work  did  not  bear  this  out. 
The  horn  (figs.  197  and  198,  inserts)  used  had  the  conical  shape,  being  30  cm. 
deep,  13  cm.  in  diameter  at  the  mouth,  and  3  cm.  at  the  base  (apex  angle  190). 
It  was  attached  to  a  telephone  (see  fig.  197,  T  and  H),  as  this  seemed  to  be 
the  only  way  of  activating  the  horn  when  air-currents  must  be  excluded. 


112 


ACOUSTIC  EXPERIMENTS  WITH  THE  PIN-HOLE 


The  attachment  was  secured  through  a  perforated  cork  and  thin  brass  tube, 
2  cm.  long  and  i  cm.  in  diameter,  flanged  and  cemented  to  the  telephone-cap. 
Thus  the  telephone-plate  was  about  2  cm.  behind  the  flat  bottom  of  the 
horn.  The  absence  of  all  constriction  might  have  been  desirable,  but  the 
data  do  not  show  it. 

Two  methods  were  used  for  sounding  the  horn  at  all  pitches.  In  the  first 
a  secondary  of  a  transformer  (fig.  197)  with  known  capacity  c  and  inductance 
L,  the  capacity  (as  usual)  being  variable  at  pleasure,  operated  the  telephone 
T  and  the  pitches  available  lay  between  a  and  a".  Higher  frequencies  were 
tested  later.  This  method  is  necessarily  discontinuous  from  capacity  to 
capacity.  The  break  B  in  the  primary  was  the  common  spring-contact  and 


it  seemed  to  suffice,  care  being  taken  not  to  change  the  tension  of  the  spring 
and  modify  the  frequency  factor.  The  horn  sounds  with  the  usual  loud 
blare,  characteristic  of  the  pitch  of  the  spring-break  and  the  pitch  to  be 
measured  is  not  heard  by  the  ear  without  special  devices.  This  is  also  for 
other  reasons  a  serious  drawback. 

In  the  second  method  (fig.  199,  insert),  a  simple  circuit  from  two  storage 
cells,  e,  with  resistance  R ,  was  periodically  broken  by  the  commutator-motor 
device  B,  the  speed  of  the  motor  being  controlled  by  a  resistance  (electric 
siren).  Both  methods  have  been  described  above.  Contact  difficulties  at  the 
commutator  are  here  not  infrequent.  The  pitch  in  this  case  must  be  deter¬ 
mined  by  the  ear  if  the  method  is  to  be  adequately  expeditious,  but  it  has  the 
advantage  of  a  continuous  method.  Frequencies  gf  to  a"  were  first  available. 
The  lower  frequencies  g  to  a'  were  added  later. 


PROBE  AND  THE  INTERFEROMETER  U-GAGE 


113 


The  pin-hole  probe  on  a  long  quill-tube,  connecting  it  with  the  U-gage, 
was  inserted  into  the  horn  at  the  place  to  be  tested. 

73.  Results  for  horn — These  are  given  in  the  graphs,  figure  197,  as 
obtained  with  the  transformer  method,  the  abscissas  showing  the  capacities 
in  microfarads  with  a  fixed  L  (about  0.38  henry)  in  the  secondary.  The  ordi¬ 
nates  are  the  acoustic  pressures  s,  measured  by  the  pin-hole  probe  when  sunk  to 
a  depth  d  below  the  mouth  of  the  horn  (s  is  roughly  in  io-6  atm.). 

What  strikes  the  eye  at  once  is  the  relative  simplicity  of  this  group  of 
curves  when  compared  with  similar  graphs  for  cylindrical  and  other  pipes. 
For  all  depths,  d,  below  the  mouth  of  the  horn,  there  is  a  dominant  crest  at 
about  (7  =  0.4  microfarad,  though  near  the  mouth  ( d  =  5,  10  cm.)  it  seems  to 
shift  slightly  into  larger  C  values  (flattens).  Only  in  case  of  d  =  30  cm.  at 
high  pitch  or  very  low  pitch  is  there  a  bulge  suggesting  a  crest  about  (7  =  0.1 
microfarad  and  above  (7  =  0.8  microfarad,  but  they  vanish  even  at  Z)  =  2  5  cm. 
Nevertheless  the  crest  is  wide  and  the  horn  suspiciously  sonorous  at  all 
pitches,  g"  to  c'. 

If  from  these  graphs  we  plot  5  against  d  for  (7  =  0.4  (near  the  crest),  the 
curve,  figure  198,  of  very  definite  character  results.  It  indicates  the  increase 
in  the  intensity  (5)  of  vibration  from  the  mouth  to  the  base  of  the  horn.  The 
rise  is  at  first  accelerated  and  finally  rapidly  retarded  toward  the  telephone 
plate.  Throughout  much  of  its  extent  it  is  nearly  straight.  The  chief  feature 
of  the  graphs  obtained  with  electric  oscillation  is  the  continuity  of  sound  at 
all  pitches.  This  continuity,  s,  in  general  increasing  as  pitch  falls,  will  in  case 
of  cylindrical  pipes  occur  even  without  a  crest. 

If  we  put  (7  =  0.4  microfarad  and  L  =  0.32+0.06  henry  and  compute  the 
frequency  as  i/n  =  2Tcy/LC  the  result  is  #g',  n  =  408.  If  (7  =  0.35  at  the  crest, 
^  =  435  or  a'  is  the  pitch.  Hence  the  pitch  of  the  horn,  so  far  as  it  can  be 
found,  lies  between  #g'  and  a'.  If  it  were  a  little  shortened,  the  latter  would 
be  acceptable. 

The  results  obtained  with  the  electric  siren,  where  the  pitch  is  directly 
and  continuously  given  by  the  ear,  are  summarized  in  figures  199  and  200. 
Here  the  currents  are  more  intense  and  the  a'  crest  for  the  pipe-depths  d  =  28 
and  25  cm.  runs  out  of  the  field.  Otherwise  its  location  is  in  correspondence 
with  its  former  C  value  and  at  d  =  io,  5,  and  2  cm.  it  again  shifts,  but  now 
to  higher  frequency. 

In  figures  199,  200,  however,  there  is  a  new  crest  near  f"  which  does  not 
appear  in  the  preceding  graphs.  It  is,  moreover,  highly  variable  with  the 
depth  d  below  the  mouth  of  the  horn,  and  is  strong  only  near  the  telephone- 
plate.  The  feature  of  these  siren  graphs  (differing  from  the  oscillation  graphs) 
is  the  occurrence  of  sharp  maxima  of  sound  between  long  intervals  of  silence. 

In  figure  201,  the  intensity  5  is  plotted  against  the  pipe-depth  d ,  for  the 
af  crest,  the  f"  crest,  and  the  b'  shift  alluded  to.  The  a'  curve  in  the  present 
cramped  scale  is  much  the  same  as  in  figure  198,  and  is  the  horn  fundamental 
regarded  as  a  closed  pipe.  The  f"  vibrates  as  if  it  were  the  first  overtone  with 


114 


ACOUSTIC  EXPERIMENTS  WITH  THE  PIN-HOLE 


two  nodal  crests,  but  enormously  dislocated  in  pitch.  With  the  transformer 
method  it  should  appear  at  C = o.  1 4  microfarad,  and  hence  if  sharp  might  be 
overlooked  between  0.1  and  0.2  microfarad  in  this  very  crowded  region.  In 
fact,  the  bulge  at  d  —  28  cm.,  C  =  0.1  microfarad  in  figure  197  is  thus  explained. 

In  figure  202,  I  have  given  the  siren-graphs  for  the  2  and  4  feet  octaves  of 
the  broad  horn,  made  at  a  somewhat  later  date.  This  work  is  difficult, 
because  the  motor-break  does  not  run  smoothly.  The  graphs  are  a  reduced 
repetition  of  those  for  the  1  and  2  feet  octaves.  As  obtained  from  a  i-foot 
horn,  figure  202  is  probably  a  response  to  the  overtones  of  the  telephone-plate 
evoked  by  the  lower  register.  Again,  f  drops  off  so  quickly  with  the  pipe- 
depth  d  that  one  suspects  it  may  be  an  incidental  note  of  the  telephone. 


Turning  to  the  transformer  graphs  197,  there  is  nothing  in  the  /'  region  to 
suggest  a  crest,  but  a  mere  decay  of  the  sound  intensity  s.  The  a  region 
could  not  be  reached.  Again,  the  continuity  of  noise  evoked  by  electric 
oscillation  contrasts  with  the  characteristic  sharp  crests  and  flat  troughs  of 
the  electric  siren. 

The  oscillation  graphs  for  intervals  of  0.01  microfarad  between  o  and  0.1 
microfarad  consisted  merely  of  a  group  of  divergent  lines  with  a  rapid  fall 
between  d  =  30  and  d  =  25  cm.  They  need  not  therefore  be  reproduced  here. 

The  divergent  results  obtained  from  the  electric-oscillation  method  and 
the  siren  pointed  to  the  spring-break  as  the  probable  cause.  The  pitch  of 
this  in  the  most  favorable  position  happened  to  be  a,  so  that  an  overtone  a' 
would  be  usually  present  in  the  spring  itself  or  in  the  telephone-plate.  In 
fact,  by  changing  the  tension  and  therefore  the  pitch  of  the  spring,  the  crests 


PROBE  AND  THE  INTERFEROMETER  U-GAGE 


115 


(some  examples  d  =  25  cm.,  const.,  are  given  in  fig.  203)  could  be  shifted  from 
about  C  =  o.35  to  even  (7  =  0.55,  a  low  C  value  for  the  crest  usually  accompany¬ 
ing  a  high  intensity  (5)  value  and  vice  versa.  In  fact,  on  further  change  of  the 
spring  it  was  even  possible  to  obtain  graphs  (for  d  =  25)  like  figure  204,  with 
three  well-defined  crests  near  #g",  #/'  and  between  d'  and  #d'.  The  graphs 
thus  depend  essentially  on  the  pitch  of  the  spring,  and  the  simple  cases  of 
figure  197  are  the  result  of  resonance  between  the  spring-break  and  the 
electric  oscillation  which  it  unlooses.  The  shift  of  crests  and  the  continued 
noise  of  the  horn  are  to  be  ascribed  to  beats  between  the  two  vibrating  systems 
in  relation  to  the  fixed  pitch  of  the  horn, 
intensities,  s,  will  be  obtained  when  this  is 
the  common  (or  octave)  pitch  throughout 
the  three  oscillations. 

To  return  to  figure  197,  of  the  three 
coupled  vibrating  systems,  two,  viz,  the 
spring-break  and  the  horn,  are  in  the  same 
key  (frequency  taken  as  a  and  a') ;  the  third, 
the  electric  oscillation,  is  varied  nominally 
over  a  wide  range  of  frequencies  (cnr  to  c'). 

It  seems  probable  that  the  massive  air- 
column  of  the  horn,  reacting  on  the  tele¬ 
phone-plate,  forces  the  electric  oscillation  to 
remain  at  the  horn  frequency  a',  with  dif¬ 
ferent  amplitudes  passing  a  maximum  when 
the  electric  oscillation  is  also  at  a',  i.  e .,  in 
resonance.  Hence  the  difference  in  figures 
197  and  199,  since  in  the  latter  no  reacting 
mechanism  is  available.  The  continuous 
noise  in  figure  197  throughout  all  frequencies 
must  thus  be  regarded  as  a  case  of  forced 
vibration  of  the  L  circuit  with  synchronism 
at  ar.  At  the  same  pitch  the  nodal  intensity  of  the  free  system  (siren,  s8) 
increases  much  faster  than  the  nodal  intensity  of  the  forced  system  (electric 
oscillation,  s0),  as  shown  by  the  graph  in  figure  201,  where  the  horizontal 
scale  s0  is  increased  four  times. 

Finally,  the  decreasing  nodal  intensity  5  toward  the  mouth  of  the  horn 
is  enhanced  by  its  increasing  sectional  area.  This  somewhat  obscures  the 
linear  relation  of  the  fringe  displacement  5  to  the  corresponding  nodal  pressure, 
as  I  shall  indicate  in  the  subsequent  section,  in  which  large  cylindrical  pipes 
are  tested. 

74.  Slender  horn — The  attempt  was  now  made  to  get  correlative  evi¬ 
dence  from  a  horn  of  smaller  angle  (figs.  205  to  210).  The  horn  in  question 
(fig.  207)  was  41  cm.  long  and  tapered  from  a  diameter  of  6.5  cm.  at  the  mouth 
to  1.5  cm.  at  the  apex  end  (angle  70),  fitting  at  once  into  the  telephone  with 


As  this  is  near  a',  the  highest 


116 


ACOUSTIC  EXPERIMENTS  WITH  THE  PIN-HOLE 


the  plate  at  44  cm.  from  the  mouth  of  the  horn.  Being  longer  than  the  broad 
horn,  it  is  thrown  off  the  a'  key.  Its  thinness  should  make  it  rich  in  overtones. 

The  graphs,  figures  205  and  206,  in  which  the  intensities  5  are  plotted 
against  the  capacity  of  the  secondary  of  the  activating  transformer  for  a  fixed 
pipe-depth  d,  show  that  overtones  are  present  in  variety  and  for  d  >  20 
cm.,  pronounced  in  character,  as  fully  revealed  by  the  curves.  Crests  are 
marked  near  C  =  o.i,  0.2,  0.3,  0.4,  0.9,  and  figure  207,  therefore,  gives  the 
intensity  at  different  depths,  d,  for  the  constant  pitch  of  the  crests  in  question, 
respectively  #g",  d",  #a\  #g',  #cf.  A  full  treatment  of  these  graphs,  though 
interesting,  would  require  too  much  space.  We  note  that  in  figure  207,  crests 
are  universal  at  pipe-depth  d=  10  cm.,  and  that  this  feature  soon  vanishes 
for  the  broad  horn  of  the  preceding  section.  Similarly  all  graphs  pass  through 
crests  at  ^  =  35  cm.,  except  the  low-pitch  curves  C  =  o.8  or  0.9  microfarad.  In 
this  case  the  horn  vibrates  as  a  closed  organ-pipe,  whereas  in  the  others,  with 


troughs  at  the  apex,  as  an  open  organ-pipe.  Between  d  =  10  cm.  and  ^  =  35 
cm.  the  detailed  progress  between  the  main  crests  is  complicated,  but  fully 
shown. 

Figure  208  gives  the  survey  in  pitch  made  with  the  electric  siren  and  ear. 
In  the  corresponding  groups,  205  and  208,  the  maxima  near  #g",  d",  gf  may 
be  taken  as  equivalent.  The  #o'  crest  at  C  =  0.3  in  figure  205  for  d  —  40  cm. 
does  not  appear,  and  may,  therefore,  be  taken  as  due  to  the  spring-break. 
The  graphs  g'  and  g",  figure  210,  are  essentially  similar  and  are  open-pipe 
curves  with  troughs  near  the  apex.  The  fifth  d"  is  a  closed  organ-pipe  curve 
with  a  crest  at  the  apex.  All  the  graphs  would  have  passed  through  crests 
at  d=  10  cm. 

Figure  210  (siren)  is  essentially  simpler  than  207  (electric  oscillation), 
which  means  that  the  ear  can  not  compete  with  pitch  determination  in  terms 
of  capacity  C,  where  detail  is  sought  for;  but  the  ear  has  nevertheless  the 
advantages  already  stated,  as  there  is  continuity  without  crowding  in  high 
pitch,  and  there  is  no  disturbing  third  vibratory  system  (spring-break). 


PROBE  AND  THE  INTERFEROMETER  U-GAGE 


117 


Hence  the  discrepancy  in  the  d"  graphs  at  pipe-depth  d  =  40  cm.,  where  the 
ear  requires  a  crest  and  the  capacity  work  a  trough,  is  interesting.  Both 
may  occur  in  this  region  of  intense  vibration,  lying  close  together.  The  g' 
and  g"  curves  of  figure  210  correspond  to  the  general  run  of  curves  in  figure 
207,  if  we  disregard  the  exceptional  cases  C  =  o.8  or  0.9  microfarad.  These 
are  much  like  d"  in  figure  210. 

75.  Cylindrical  pipe — 'This  was  28  cm.  long  and  2.8  cm.  in  diameter 
(fig.  213,  insert),  with  the  plate  of  the  telephone  34  cm.  below  the  mouth  of 
the  pipe.  The  transformer  graphs  s,  C  are  given  in  figures  211  and  212, 
with  detail  measurements  between  C—o  and  0.1  microfarad  in  figures  213  and 


214,  for  all  pipe  depths,  d  =  o  to  28  cm.  The  curves  of  the  broad  horn  are 
reduced  to  the  same  scale  in  the  first  figure,  for  comparison.  When  blown, 
the  pipe  responded  to  d'}  which  implies  overtones  at  a"  and  above. 

Owing  to  the  high  intensities,  small  crests  are  possibly  drawn  out  and 
less  apparent;  but  the  general  detail  is  much  greater  than  in  the  preceding 
work  with  horns.  There  is  a  continued  increase  of  intensity,  s,  when  the 
pitch  is  being  continually  lowered,  and  in  this  respect  these  graphs  again 
differ  radically  from  the  tests  with  the  electric  siren  presently  to  be  given. 
Nowhere  is  there  an  approach  to  silence.  As  a  whole,  the  graphs  suggest  that 
a  smoothed  common  crest  of  spring-break  and  pipe  oscillation  is  absent  and 
therefore  the  electric  oscillation  finds  no  steady  oscillation  with  which  to 
resonate. 

Owing  to  the  excessive  ornamentation  of  the  graphs,  I  have  made  sections 


118 


ACOUSTIC  EXPERIMENTS  WITH  THE  PIN-HOLE 


(in  5  and  d  for  constant  C )  only  at  C  =  o.i,  0.3,  and  1.0  microfarad,  and  these 
graphs  are  given  in  figure  215,  corresponding  to  the  notes  #g",  #a',  and  c'. 
The  low  note  c'  falls  rapidly  as  the  mouth  of  one  pipe  is  approached,  from  its 
high  initial  intensity.  The  three  curves  and  others  which  might  be  added  are 
all  different  from  each  other,  and  hard  to  construe.  It  looks  as  if  beating 
wave-trains  had  been  encountered. 

A  much  more  serviceable  general  result  is  obtained  with  the  electric 
siren,  and  these  graphs  for  intensity  5  and  pitch  are  given  in  figures  216  and 
217.  Crests  at  a',  e",  and  a"  are  prominent,  though  there  are  some  humps 
and  minor  crests.  The  intensity  of  these  crests  is  sustained  very  nearly  to 
the  mouth  of  the  cylindrical  tube,  at  least  as  far  as  d  =  5  cm.  The  records 


for  a  d'  pipe  are  puzzling;  but  a",  the  first  overtone  of  d'f  is  probably  awakened 
both  by  the  a '  and  the  g"  of  the  siren,  while  the  e"  will  presently  appear  as 
an  open  organ-pipe  harmonic. 

The  corresponding  5  and  d  graphs  are  found  in  figure  218  and  can  not  be 
correlated  with  the  transformer  set  (215),  where  they  would,  moreover,  be 
in  the  crowded  region.  The  new  graphs  for  a'  and  a"  are  of  the  same  nature 
(having  the  same  crest  and  trough),  except  near  the  bottom,  d  =  28  cm., 
where  the  conditions  are  no  doubt  complicated  by  the  nearness  of  the  tele¬ 
phone-plate.  The  e"  graph  differs  from  them  radically  and  is  probably  an 
open  organ-pipe  graph.  This  loses  its  intensity  rapidly  from  the  middle 
toward  the  mouth  (^<15  cm.),  whereas  the  a!  and  a"  graphs  carry  their 
high  5  to  within  d  —  5  cm.  Finally,  a"  has  been  recognized  as  the  first  overtone 
of  the  d'  pipe-note  and  the  a'  partakes  of  the  same  form,  as  already  instanced. 


PROBE  AND  THE  INTERFEROMETER  U-GAGE 


119 


One  might  suppose  that  by  decreasing  the  steps  in  C  to  o.oi  microfarad, 
salient  high-pitch  maxima  would  appear  in  the  transformer  graphs.  Figures 
213  and  214  show  that  this  is  not  the  case.  The  period  of  coherence  of  the 
transformer  oscillations  is  either  too  short  or  the  successive  impulses  are  out 
of  step  with  each  other  and  interfere  in  their  integration  by  the  pipe.  If  T 
is  the  period  of  the  oscillation,  xT  the  period  of  coherence,  and  T’  the  period 
of  the  break  circuit,  then  T'—xT  is  the  interval  without  stimulation.  The 
binominal  increases  for  a  given  xt  as  T  is  smaller,  and  one  may  therefore  look 
for  increased  intensity  5  as  T  is  larger.  This  is  in  conformity  with  all  the 
transformer  graphs,  even  for  the  cylindrical  pipe. 


Experiments  were  made  with  the  much  slower  (frequency)  mercury  break, 
but  the  5  values  were  too  small.  An  example  is  given  in  figure  204.  The 
crest  at  C  =  o.4  microfarad  is  too  flat  and  beyond  C  =  0.6  microfarad  s  is 
practically  constant.  Four  storage  cells  were  used  in  the  primary. 

76.  Extensible  pipe — Since  there  are  three  vibrating  systems  in  the  trans¬ 
former  method,  two  of  them  should  be  made  adjustable  if  the  third  is  given  to 
obtain  the  largest  acoustic  pressure  values  (s).  An  extension  was  therefore 
added  to  the  pipe  so  that  its  length  could  be  increased  continuously,  from 
d  =  28  (note  d')  to  35  cm.  (note  b).  By  setting  this  for  a  maximum  5  at  any 
C ,  the  remainder  of  the  curve  was  then  worked  out.  A  remarkable  result 
presented  itself,  with  an  important  bearing  on  the  pin-hole  probe,  inasmuch 
as  the  graphs  now  consisted  of  right-line  elements  between  breaks. 

In  figure  219  the  largest  5  was  first  established  by  tuning  for  the  pipe- 
depth,  d  =  30  cm.  (the  probe  being  at  the  bottom  of  the  tube,  as  usual).  The 
graph  obtained  for  varying  C  (o  to  1.1  microfarads)  starts  with  a  linear  sweep 
as  far  as  C  =  0.3  microfarad  (a'),  then  bends  abruptly  to  a  second  linear  sweep 
9 


120 


ACOUSTIC  EXPERIMENTS  WITH  THE  PIN-HOLE 


as  far  as  C—  0.9  microfarad,  after  which  the  course  is  curved  to  the  crest 
beyond  the  figure. 

It  seems  obvious  that  each  of  these  lines  corresponds  to  a  given  kind 
of  vibration,  i.  e.,  to  a  given  overtone  which  breaks  abruptly  into  the  next 
available  overtone. 

The  behavior  of  the  untuned  pipe  {d  =  28  cm.)  for  the  given  spring-tension 
is  shown  in  the  lower  curve.  There  is  a  break  at  C  =  0.2  ( d ")  and  at  C—  1.0 
(c')  microfarad.  In  the  repetition  (black  circles)  the  break  at  C  =  0.7  (#d') 
is  probably  an  accidental  small  change  in  the  tension  of  the  electrical  spring- 
break.  Between  these  points  the  graph  is  strikingly  linear. 

After  the  tube  was  further  elongated  to  the  pipe-depth  3  5  cm.  (now  nearly 
in  resonance  with  the  spring-break),  where  a  second  and  much  stronger  maxi¬ 


mum  (fig.  220)  appeared.  The  rectilinear  progress  between  C  =  o.i  to  0.3, 
0.4  to  0.6,  0.6  to  0.9,  0.8  to  1.2,  1.3  to  1.5,  1.6  to  2.0  microfarads  is  throughout 
marked.  Even  near  the  crest  C=  1.2  the  tendency  is  still  observable.  This 
relatively  enormous  crest  (5  =  475)  is  in  keeping  with  the  near  resonance  of 
spring-break,  organ-pipe,  and  electric  oscillation. 

It  seemed  worth  while  to  test  the  case  further  with  untuned  lengths  be¬ 
tween  d  =  28  cm.  and  ^  =  34  cm.,  and  throughout  large  C  ranges  (o  to  2  micro¬ 
farads).  The  graphs  are  given  in  figures  221  and  222  for  an  altered  transformer¬ 
spring  tension.  The  case  for  d  =  2  8  now  turns  out  quite  differently  from 
figure  219,  but  this  is  the  necessary  result  for  modified  spring-tension  or 
pitch.  Broken  rectilinear  paths  are  the  rule  for  d  =  28,  29,  31,  33.  The  two 
latter,  with  their  roof -like  crests,  are  astonishing.  The  graph  for  ^  =  34  (very 
near  the  maximum  ^  =  35)  points  at  highly  unstable  conditions  of  vibration. 
Split  crests  like  this  one  between  C  =  o.4  and  0.8  are  rare. 


PROBE  AND  THE  INTERFEROMETER  U-GAGE 


121 


Finally,  in  figure  223,  for  the  optimum  ^  =  35,  the  successively  tuned 
pipe  is  compared  with  the  untuned  pipe.  Below  <7  =  0.5  the  divergence  is 
not  large,  both  starting  under  tuned  conditions.  Thereafter  the  divergence 
rapidly  increases,  the  tuned  pipe  naturally  being  in  excess.  From  C  =  0.8 
on,  passage  of  the  untuned  («)  condition  to  the  tuned  condition  (t)  is  indicated 
by  arrows.  To  get  the  maximum  5  values  it  is  thus  necessary  to  retune  the 
pipe  at  all  pitches.  Linear  progression  is  a  characteristic  chiefly  of  the  untuned 
pipe.  One  may  note  that  successive  tuning  (resonance  throughout)  has 
raised  the  crest  to  nearly  5  =  550  (over  0.4  mm.  of  mercury). 


The  same  figure  shows  the  corresponding  behavior  at  the  smaller  maximum 
at  d  =  31.  Linear  progress  is  interrupted  by  the  tuning  indicated  by  the 
arrows. 

77.  Closed  organ-pipe — 'The  open-mouthed  organ-pipe  is  very  noisy,  so 
that  in  this  respect  the  doubly  closed  organ-pipe  shown  in  the  insert,  figure 
224,  is  preferable.  Here  p  is  the  pipe  27  cm.  long  in  the  clear,  T  the 
attached  activating  telephone,  and  be  the  pin-hole  probe.  The  point  c  may 
either  be  thrust  to  the  rear,  near  the  telephone,  or  (as  in  figure)  the  pin-hole 
c  may  be  near  the  front  of  the  tube.  This  should  make  no  difference  in  the 
acoustic  pressure  5,  other  things  being  equal.  The  telephone  T  was  activated 
by  the  transformer  method,  as  the  specific  results  of  this  method  are  partic¬ 
ularly  in  question. 

The  graphs  1  and  3  (the  former  raised  for  clearness),  for  the  same  tense 
spring-break  adjustment  left  unchanged,  but  with  the  pin-hole  respectively 


122 


ACOUSTIC  EXPERIMENTS  WITH  THE  PIN-HOLE 


in  the  rear  (bottom)  and  in  the  front  of  the  doubly  closed  tube,  are  practically 
identical.  They  again  consist  of  linear  parts  (as  above),  with  abrupt  breaks. 
Each  exhibits  two  crests,  respectively  above  a'  and  near  #d'. 

The  graph  2  with  a  loose  spring-break  differs  from  1,  and  graph  4  differs 
both  in  intensity  and  character  from  all  the  graphs.  But  this  is  due  to  the 
fact  that  the  spring-break  has  to  be  reset  (frequency  change)  and  not  to  the 
fore-and-aft  positions  of  the  pin-hole.  While  in  graph  4  the  #d'  crest  is 
marked,  it  is  quite  absent  in  graph  2.  In  both  the  #a'  crest  is  abortive,  partic¬ 
ularly  in  4. 

The  endeavor  to  tune  the  pipe  by  adding  an  extension  (fig.  225,  inset) 
was  not  very  successful,  probably  because  the  slide- joint  at  the  draw-tube 


can  not  conveniently  be  made  tight.  The  greatest  intensities  were  obtained 
for  pipe-depth  d  =  29  cm.  and  the  figure  in  the  upper  graphs  shows  two  inde¬ 
pendent  results.  The  crests  at  #a'  and  d!  are  accentuated,  all  being  har¬ 
monics  of  the  spring-break  pitch.  The  elongated  tube  ^  =  35  cm.  (lower 
curve  gives  an  example)  merely  adduces  a  case  of  weak  repetition.  After 
tuning  the  spring-break  by  reducing  its  tension,  the  intermediate  graphs 
(fig.  225,  ^  =  35  cm.)  were  obtained  in  successive  experiments.  The  crest 
has  fallen  in  pitch  (#g')  and  the  harmonic  near  df  is  practically  absent.  It  is 
generally  preferable,  therefore,  to  select  a  suitable  fixed  length  of  pipe  p 
and  to  tune  the  spring-break  in  conformity  if  high  5  values  are  sought. 

78.  Alternating  current — The  attempt  to  energize  the  primary  of  the 
induction  coil  by  an  alternating  current  proved  unsatisfactory  for  the  reason 


PROBE  AND  THE  INTERFEROMETER  U-GAGE 


123 


that  while  the  induction  is  relatively  feeble  as  compared  with  the  break-  * 
circuit  methods  used  heretofore,  the  heating  effect  of  these  continuous  cur¬ 
rents  is  out  of  all  proportion.  The  current  for  the  primary  was  obtained  by 
stopping  down  the  no- volt  lighting  circuit  with  a  resistance  of  about  20 
ohms,  not  including  the  impedance  of  the  primary.  The  frequency  of  the 
secondary  was  modified  as  before  by  changing  the  capacity  C  from  o  to  1.1 
microfarads.  The  results  so  obtained  are  summarized  in  figures  226  and  227. 
The  curves  are  interesting  as  a  whole,  as  they  consist  conspicuously  of  right¬ 
line  elements,  with  breaks  between  C—  0.6  and  0.7  and  others  near  C  —  3 
microfarads. 


In  case  a  (pipe  and  alternating  current  in  the  same  key)  the  obser¬ 
vations  were  begun  at  (7=1.0  microfarad  and  finished  as  expeditiously  as 
possible  to  keep  the  wires  cool.  After  completing  the  series,  the  drop  of  5 
at  C=i.o  (see  figure)  was  about  one-seventh  of  the  full  deflection,  5  =  70. 
In  case  b  the  progress  of  observation  was  in  the  reverse  direction  of  increasing 
C.  The  graph,  partly  for  this  reason  and  partly  because  of  less  perfect  tuning, 
is  much  lower,  though  the  two  independent  series  made  are  practically  coinci¬ 
dent  and  show  the  same  peculiar  break  between  C—  0.6  and  0.7  microfarad. 
In  case  C  the  tuning  is  still  less  perfect  and  the  break  at  C  —  0.6  is  just 
perceptible. 

The  tuning  of  the  pipe  must  be  done  with  nicety  and  requires  an  adjust¬ 
ment  of  pipe-length  to  within  a  millimeter.  As  the  alternating  current  makes 
60  cycles  per  second,  the  harmonics  of  the  key  of  B~l  are  in  question.  The 
curve  d  (raised  5  =  20)  was  obtained  from  a  pipe  specially  adapted  for  timing, 


124 


ACOUSTIC  EXPERIMENTS  WITH  THE  PIN-HOLE 


with  wires  cooled  after  long  waiting;  in  case  of  e  the  wires  had  been  used 
and  were  warmer.  There  is  here  an  additional  break  at  C=i.o.  At  C  =  o.i 
there  is  scarcely  any  perceptible  deflection,  so  that  the  graphs  start  their 
upward  sweep  abruptly  about  at  this  point.  The  curves  are  chiefly  interesting 
because  of  the  sharp  breaks  between  linear  elements,  and  an  investigation  of 
the  relations  of  successive  values  of  ds/dC  with  their  relation  to  frequency 
is  again  suggested. 


79.  Remarks — In  my  work  heretofore  I  have  associated  the  fringe  dis¬ 
placement  5,  i.  e .,  the  nodal  intensity  or  acoustic  pressure,  with  the  usual 


energy  {E  per  unit  of  volume)  equation.  If  n  is  the  frequency  and  a  the  ampli¬ 
tude  of  the  sound-wave,  we  may  therefore  write 

E  =  p-\-  pv2/2  =&s+(p/2)a247rV 

At  the  mouth  of  the  tube  5  is  zero  and  a  the  maximum;  at  the  bottom  or 
node,  a  is  zero  and  5  a  maximum.  The  expectation  that  a  similar  equation 
could  also  be  used  to  interpret  the  fringe  displacement  at  a  given  point  for 
different  frequencies  is  not  warranted.  For  if  we  put  47r2n2  =  i/LC,  p  =  ks , 
and  assume  E  to  be  constant  along  the  linear  elements  of  the  graphs,  the 
result  is  (s— s')  =  (p/2 KL)  ( a2/C—a'2/C' ),  whereas  the  graphs  suggest  As*  AC 
simply,  along  each  element. 

The  view  that  the  oscillation  frequency  («)  of  the  organ-pipe  is  impressed 
on  the  oscillation  frequency  («')  of  the  secondary  actuating  the  telephone- 


PROBE  AND  THE  INTERFEROMETER  U-GAGE 


12o 


plate  is  also  unsatisfactory.  For  if  Y  is  the  amplitude  of  the  electric  circuit 
under  a  harmonic  electromotive  force  E  cos  c ot, 

Y  =E/\ /  (a/2  — CO2)2  +  k20)2 

where  00  =  27 m  and  co'  =  2 tu'  are  the  angular  frequencies  of  the  free  and  fric¬ 
tionless  acoustic  and  electrical  circuits,  respectively,  and  K  is  the  coefficient 
of  friction.  This  may,  as  usual,  be  reduced  to  proportionalities  in  the  form 

F  =  i/V/(i-%2)2  +  q:¥  where  a  =  K/<ar,  y  =  Y/(E/u /2),  jc  =  «/&/.  This  y 
has  a  crest  for  x2  =  1  —  a2/ 2 . 

If  co'  =  i/LC  and  K  is  relatively  very  small,  the  equation  reduces  to 

y  =  (I  _  (JM£  \  %) 

i-o?LC  \i-u2LCj 

approximately,  where  co,  K,  L  are  constant  and  C  variable.  Hence,  even  if 
we  neglect  the  term  in  K  and  associate  Y  with  the  fringe  displacement  5,  an 
equation  in  this  form  is  not  serviceable  in  identifying  As  oc  AC  along  linear 
elements,  unless  c c2LC  is  small  compared  with  1.  This  would  not  be  the  case 
with  the  fundamental  or  any  harmonics  of  the  cylindrical  pipe.  Even  if  co 
refers  to  the  frequency  of  the  spring-break  taken  at  pitch  a,  the  equation 
remains  inapplicable. 

This  suggests  a  simpler  approach  through  the  capacity  equation  Q  =  CV, 
whence  As  oc  At  =  (dV/dt)AC;  or  the  slopes  of  the  linear  elements  of  the  graphs 
are  to  be  associated  with  the  effective  time-rate  at  which  the  potential  of  the 
condenser  changes.  The  value  of  dV/dt  depends  on  the  form  of  residual  wave 
on  which  the  new  impulse  is  superimposed.  Moreover,  a  reason  for  the 
broken  linear  relations  of  s  and  C  is  now  apparent,  for  the  fringe  displacement 
s  measures  the  difference  of  level  of  the  surfaces  of  mercury  in  the  U-gage. 
It,  therefore,  also  measures  the  potential  energy  localized  in  the  stationary 
wave  at  the  point  of  the  pin-hole  probe,  though  it  does  this  with  a  coefficient 
which  may  be  either  positive  or  negative.  The  stream-lines  run  from  the 
outside  to  the  inside  of  the  pin-hole  embouchure. 

80.  Charging  circuit — Following  the  suggestion  at  the  end  of  the  last 
section,  a  change  of  circuit  was  chosen  in  which  the  condenser  C  (fig.  230, 
insert)  is  charged  directly  an  open  circuit.  Here  B  is  the  spring-break  (con¬ 
veniently  kept  in  resonance  with  the  lighting  circuit  in  the  key  of  B),  E  and 
R  electromotive  force  (2  cells)  and  resistance,  T,  p,  telephone  and  organ-pipe, 
I,  II,  primary  and  secondary  of  the  transformer.  When  B  is  open,  C  is  charged 
by  E  and  discharged  on  closing.  The  coils  I  and  II  were  eventually  to  be 
removed. 

Figure  230  shows  the  sC  graphs  for  the  intervals  o  to  1.1  microfarads. 
These  are  successive  measurements,  each  graph  (1,  2,  3,  4)  being  in  turn 
moved  0.1  microfarad  to  the  right  for  clearness.  The  pipe  was  carefully 
tuned  for  the  largest  5  available,  in  all  cases.  The  results  are  a  set  of  data 
strikingly  linear  and  parallel  in  their  main  features,  except  for  the  occurrence, 


126 


ACOUSTIC  EXPERIMENTS  WITH  THE  PIN-HOLE 


almost  capriciously,  of  the  breaks  indicated  by  the  arrows.  As  the  spring 
interrupter  was  kept  in  tune  (beats),  the  breaks  in  question  are  results  of 
an  accidental  intonation  of  another  harmonic,  as  soon  as  the  conditions 
for  it  are  at  hand,  or  the  instability  of  the  original  harmonic  is  excessive. 
This  happens  for  capacities  below  0.5  microfarad,  while  0.4  microfarad  usually 
suffices  for  the  breakdown. 

It  seemed  desirable  to  determine  how  far  this  behavior  would  be  pro¬ 
longed,  and  in  figure  229,  the  graphs  5,  6,  and  7  are  worked  out  between  C  —  0.9 
and  2.2  microfarads,  and  in  No.  8  between  o  and  2.2  microfarads.  The  ten¬ 
dency  to  linear  and  parallel  variation  persists;  but  the  breaks  occur  far  more 
capriciously,  as  one  would  expect  for  these  regions  of  low  pitch.  No.  7  after 


C— 1.5  microfarads  breaks  almost  to  the  horizontal.  No.  8,  where  the  whole 
interval  is  tried  out,  is  interesting,  as  the  slope  of  the  line  at  the  lower  and 
at  the  top  end  are  about  the  same  (see  dotted  line).  One  also  notes  that 
after  these  breaks  the  curve  does  not  recover,  but  the  s  remains  continuously 
below  the  prolongation  of  the  lower  part  of  the  curve.  This  would  also  be 
expected,  since  the  fringe  displacement  5  measures  the  difference  of  level  of 
the  mercury  surfaces  of  the  U-gage  and  hence  the  wave-energy  potentialized 
at  the  pin-hole.  Each  new  increment  is  added  to  the  stored  energy  or  may 
also  be  withdrawn  from  it,  as  in  figures  221,  222,  and  223  for  instance,  fol¬ 
lowing  the  crest. 

In  figure  228,  the  results  are  given  for  cases  in  which  the  primary  (insert, 
fig.  230)  or  secondary,  or  both  primary  and  secondary,  are  removed,  the  pipe 
being  tuned  for  each  case,  separately.  With  the  primary  only  in  circuit 


PROBE  AND  THE  INTERFEROMETER  U-GAGE 


127 


(secondary  removed)  a  distinctly  higher  pitch  was  heard,  though  the  pipe- 
depth  is  about  the  same.  In  this  case  and  when  both  I  and  II  are  cut  out, 
the  graphs  have  definite  crests,  and  these  graphs  are  as  a  whole  more  curvili¬ 
near  than  the  preceding.  With  II  only  in  place,  the  largest  fringe  displace¬ 
ments,  5,  obtainable  are  too  small  to  be  of  much  service.  In  fact,  taken 
together,  these  graphs  are  throughout  small  in  their  5  values,  as  compared 
with  figures  229  and  230,  with  both  I  and  II  in  place;  and  the  latter,  in  turn, 
4  to  5  times  less  in  sensitiveness  than  the  above  graphs  for  a  completely 
separated  primary  and  secondary.  The  marked  tendency  to  preserve  linear 
progress  in  the  present  cases  has,  however,  been  put  in  evidence. 


81.  Reentrant  pin-hole  probe — -At  the  present  stage  of  research,  a  deter¬ 
mination  of  the  correlative  behavior  of  the  reentrant  pin-hole  probe  is  per¬ 
tinent.  Accordingly  the  cylindrical  pipe  of  length  29.3  cm.  and  diameter  2.8 
cm.  activated  by  the  telephone  (as  above)  was  chosen;  but  the  pin-hole  probe 
be  (fig.  232,  insert)  now  carried  a  reversed  pin-hole  at  c.  As  this  was  a  sensi¬ 
tive  glass  cone,  it  ended  in  a  quill-tube  at  its  farther  end,  the  whole  being 
about  2  cm.  long  from  the  pin-hole.  The  quill-tube  mouth  was  in  all  cases 
placed  about  1  cm.  from  the  bottom  of  the  pipe  p. 

The  sC  curves  were  first  worked  out  for  the  salient  adjustment  of  pin-hole 
and  the  results  are  given  in  figure  231.  There  is  a  very  definite  crest  at  C  =  1 .4 
microfarads,  about,  as  shown  by  the  smaller  curves,  giving  the  details  between 
o  and  0.1  microfarad  and  0.1  and  0.2  microfarad.  The  trough  is  equally 
definite  at  about  £7  =  3.5  microfarads. 


128 


ACOUSTIC  EXPERIMENTS  WITH  THE  PIN-HOLE 


The  pin-hole  end  was  now  reversed  and  the  results  of  figure  232  (two  runs) 
were  obtained.  Thus  the  reentrant  pin-hole  probe  is  astonishingly  sensitive, 
the  s  values  being  even  larger  than  in  the  preceding  salient  case.  The  negative 
crest  at  C=  1.4  and  negative  trough  at  £  =  3.4  also  appear  clearly;  but  they  are 
not  nearly  so  salient  as  in  figure  231  and  there  is  less  tendency  toward  a  limit 
of  5  beyond  C=  1 . 1  microfarad. 

Thus  one  is  urged  to  ascertain  how  this  strong  response  will  vary,  if  the 
quill-tube  shaft  of  the  pin-hole  is  gradually  lengthened,  as  in  the  insert,  figure 
235  or  238,  where  p  is  the  organ-pipe  with  the  mouth  of  the  quill-tube  (as 
before)  1  cm.  from  the  bottom  of  the  pipe  p  (U-gage  being  beyond  b ),  but  with 
the  reversed  pin-hole  at  a  distance  £  from  the  bottom.  This  x  is  successively 
enlarged,  till  it  reaches  beyond  the  length  of  the  pipe  p. 


The  graphs  for  each  x  are  worked  out  (5  plotted  positively  downward) 
and  given  in  figures  233,  234,  235,  and  236.  Far  from  losing  in  value,  the 
sensitivity  (5)  increases  with  x  periodically  and  to  such  an  extent  that  an 
enlarged  scale  had  to  be  adopted  in  the  figures.  The  graphs,  figures  233  and 
234,  moreover,  show  two  initial  negative  crests  (owing  probably  to  incidental 
change  of  the  pitch  of  the  spring-break  as  compared  with  the  case  of  figures 
231  and  232),  at  C—  1.4  and  3.5  microfarads,  about,  beyond  which  they  tend 
to  decrease,  as  a  rule,  but  at  C  =  0.9  (roughly)  the  suggestion  of  a  trough 
at  #  =  3.5  cm.  passes  into  a  crest  at  x  =  io,  12,  14  cm.  At  £  =  16,  the  initial 
trough  at  C=  1.5  microfarads  only  tends  to  survive  and  the  others  to  vanish. 
This  behavior  is  kept  up  in  figure  235  for  #  =  16.5,  19,  21,  23.  With  #  =  25.5 
27.5,  29.5,  however,  the  crest  at  C  =  o.9  microfarad  is  again  introduced,  so 


PROBE  AND  THE  INTERFEROMETER  U-GAGE 


129 


that  it  appears  and  disappears,  periodically.  In  figure  236  the  crest  at  C=  1.5 
microfarads  is  very  distinct,  as  it  has  been  throughout,  while  for  £  =  29.5 
and  perhaps  2  =  25.5  there  is  a  strong  suggestion  of  the  reappearance  of  the 
crest  at  £  =  3.5  microfarads.  A  certain  capriciousness  in  the  intonation  is  of 
course  to  be  expected. 

82.  The  same ;  s  and  x  graphs — The  relation  of  nodal  intensity  5  to  the 
distance  x  of  the  pin-hole  from  the  bottom  of  the  pipe  ( p )  is  an  interesting 
interpretative  relation.  It  is  given,  so  far  as  possible,  in  figure  237.  Unfor¬ 
tunately,  measurements  at  the  first  crest  at  C=  1.5  microfarads  were  not 
included.  I  shall,  therefore,  have  to  consider  the  relations  for  C  =  o.i  and 
C  =  o.2,  though  these  leave  much  to  be  desired,  even  if  they  include  the  crest 


between  them.  The  two  graphs  suggest  a  crest  at  about  2  =  12  cm.  and  at 
the  end  of  the  pipe  2  =  29.5  cm.  and  a  trough  at  about  2  =  20  cm.  Since  the 
quill-tube  attached  to  the  pin-hole  extends  to  1  cm.  of  the  bottom  of  the 
pipe  p,  this  makes  the  quill-tube  length  5  trailing  the  pin-hole,  5=2— 1, 
so  that  one  may  suspect  that  crests  alternating  with  troughs  lie  at  one-third, 
two-thirds,  and  three-thirds  of  the  length  of  the  quill-tube. 

There  is,  however,  an  additional  crest  in  the  Cs  graphs,  i.  e.,  the  fluctuat¬ 
ing  and  flat  crest  at  about  C  =  o.g  microfarad.  The  relations  of  this  in  its 
sx  graphs  are  also  given  in  figure  237,  and  fully  corroborate  the  inferences 
drawn,  except  in  so  far  as  the  first  crest  at  2  =  1 1  cm.  is  higher  than  the  second 
at  2  =  30,  about.  The  graph,  however,  considering  the  difficulties  encountered , 
is  remarkably  definite  as  a  whole.  The  trough  is  again  at  2  =  2 1  cm. 

Whether  the  crest  at  5  =  10  cm.  stimulates  the  crest  above  5  =  28.5  cm. 
or  the  reverse,  or  whether  both  are  directly  evoked,  will  have  to  be  specially 
examined;  but  the  extremely  curious  fact  is  brought  out  by  these  graphs 


130 


ACOUSTIC  EXPERIMENTS  WITH  THE  PIN-HOLE 


(fig.  237)  that  the  narrow  quill-tube  of  diameter  0.35  cm.  vibrates  like  a  closed 
organ-pipe  with  a  pin-hole  embouchure  and  exactly  like  the  surrounding 
wide  brass  closed  organ-pipe  2.8  cm.  in  diameter,  even  when  the  lengths 
of  both  are  nearly  30  cm.  Furthermore,  the  node  at  the  bottom  of  the  brass 
pipe  p  (fig.  237,  insert)  corresponds  to  the  ventral  segment  at  the  mouth  c  of 
the  quill-tube  pipe,  be,  and  the  node  of  the  latter  at  g  to  the  ventral  segment 
of  the  brass  pipe,  particularly  when  g  lies  at  the  mouth  of  p.  Pipe  node  thus 
becomes  a  quill- tube  ventral  segment;  i.  e.,  the  pressure  increasing  from  the 
mouth  of  the  bottom  of  p  and  surrounding  the  quill-tube  (therefore  not 
affecting  the  slender  air-column  within),  finds  a  sudden  release  at  the  mouth 
if  the  quill-tube  c ,  and  a  wave  opposite  in  phase  passes  up  the  quill-tube,  so 
that  the  inside  of  the  pin-hole  and  the  bottom  of  the  brass  pipe  are  the  seats 
of  corresponding  nodes.  Together  they  constitute  a  doubly  closed  pipe, 
telescoped  to  one-half  its  normal  length. 


83.  The  same.  Direct  tests — To  test  the  question  further,  I  made 
direct  measurements  (keeping  C=  1.5  microfarads  the  position  of  the  initial 
crest)  with  the  same  apparatus,  but  using  the  slide  micrometer  instead  of  the 
ocular  micrometer  (s)  and  the  graph  of  r  (in  io-3  cm.)  and  x  is  given  in  figure 
238.  Here  we  have  a  distinctly  marked  crest  at  5  =  %— 1  =  10  cm. ,  and  a  trough 
at  5  =  20  cm.  The  second  crest  beyond  x  =  28.5  cm.  is  again  less  intense  than 
the  nearer  one. 

The  question  now  occurs  as  to  how  far  this  interesting  periodic  relation 
may  be  expected  to  go;  whether  it  will  still  be  marked  after  the  quill-tube 
length  gc  exceeds  the  length  of  the  pipe  p.  Accordingly,  the  apparatus  was 
overhauled,  freshly  tuned,  and  better  facilities  for  measuring  the  lengths  x 
from  pin-hole  to  the  bottom  of  p,  were  provided.  As  before,  the  mouth  of 
be  at  c  is  kept  1  cm.  from  the  bottom  of  p,  so  that  quill-tube  length  is  8  =%  —  1 
cm.  Figure  239  shows  the  data  (r,  x)  as  given  by  the  slide  micrometer. 
The  striking  result  is  obtained  that  the  periodicity  practically  vanishes  soon 
after  (at  £  =  37  cm.)  the  pin-hole  lies  outside  of  the  surrounding  brass  tube 


PROBE  AND  THE  INTERFEROMETER  U-GAGE 


131 


of  length  29  cm.,  for  between  *  =  37  and  45  cm.  the  r  is  constant.  Hence,  a 
trailing  quill-tube  or  rubber  hose  of  this  length  should  be  used  if  the  pin-hole 
probe  is  to  serve  for  pitch  determination  apart  from  its  own  pitch  prefer¬ 
ences.  Moreover,  if  the  evanescent  trough  and  crest  at  *  =  35  and  37  cm. 
respectively,  may  be  included,  the  distance  between  trough  and  crest  (semi 
wave-length)  diminishes  rapidly  as  well  as  the  amplitude,  r.  Crests  project 
farther  above  the  final  mean  altitude  r  than  the  troughs  fall  below  it. 
The  values  for  crests  and  troughs,  so  far  as  these  can  be  made  out,  are  again 
5  =  10,  20,  29  cm. 


84.  Plate  pin-hole  with  anterior  and  posterior  quill-tubes — The  very 
definite  contrast  obtained  in  the  results  of  the  salient  and  reentrant  position 
of  the  glass  (conical)  pin-hole  probe  suggested  similar  experiments  with  a 
pin-hole  pierced  in  a  soft,  thin  metal  plate  (copper  or  aluminum),  with  the 
two  sides  as  nearly  identical  as  possible.  As  shown  in  figure  240,  this  plate 
g  is  cemented  between  two  lengths  of  quill-tube  b  g  and  g  c,  c  being  open  and 
kept  at  1  cm.,  from  the  bottom  of  the  pipe  p,  actuated  by  the  telephone.  The 
fixed  quill-tube  b  g  was  30  cm.  long  and  joined  at  b  with  thin  rubber  pipe  of 
about  the  same  diameter,  and  over  50  cm.  long,  connecting  b  with  U-gage 
beyond.  The  length  g  c  (open  at  c)  was  variable  and  increased  in  steps  of 
2  cm.  from  o  to  28  cm.,  the  pipe  p  being  29  cm.  long.  Quill-tube  lengths  were 
thus  8  =  x  —  i.  My  expectation  was  that  the  initial  positive  nodal  pressure 
would  eventually  be  quite  wiped  out  and  become  negative,  since  the  probe 
g  c  (counteracting  b  g  salient)  is  reentrant.  It  was,  therefore,  astonishing  to 
find  the  original  positive  pressure  not  only  remaining  positive,  but  increasing 
(periodically)  as  the  length  of  the  reentrant  probe  g  c  increased.  This  shows 


132 


ACOUSTIC  EXPERIMENTS  WITH  THE  PIN-HOLE 


that  the  occurrence  of  a  node  in  the  pin-hole  probe  near  the  pin-hole  is  not 
necessarily  coincident  with  the  occurrence  of  excess  pressure  on  the  same  side, 
as  I  have  usually  supposed.  In  fact,  it  will  now  appear  that  the  two  sides  of 
any  pin-hole  are  specifically  different,  so  that,  for  instance,  an  air-current 
passing  through  in  one  direction  might  do  so  without  break  in  the  continuity 
of  the  jet,  whereas,  if  passing  through  in  the  other  direction,  the  jet  might 
break  up  into  turbulent  motion.  These  initial  differences  would  then  be 
enhanced  by  favorable  acoustic  conditions  of  length,  etc.,  or  the  reverse. 

The  5  C  graphs  for  a  pin-hole  about  0.035  cm.  in  diameter  pricked  in  thin 
copper  foil  from  the  outside  are  given  in  figures  240,  241,  and  242,  for  values 
of  x  —  1  =  5  from  o  to  28  cm.  The  added  quill-tubes  were  0.35  cm.  in  diameter. 


The  graphs  for  5  =  o,  2,  4,  6  cm.,  figure  240,  are  similar  in  character,  but  with 
8  =  8  cm.  a  change  enters,  so  that  intersections  occur.  The  dominating  crest 
is  near  C  =  o.i  microfarad,  a  weaker  one  at  about  C  —  2.5  microfarads,  and  a 
final  one  beyond  C=  1.1  microfarads.  The  trough  is  near  C  =  0.6  microfarad, 
but  shifts  continually  and  periodically. 

In  figure  241,  the  graphs  for  #—1  =  6  =  8,  10,  12,  14,  16  are  exhibited,  5  =  8 
and  10  being  nearly  the  same.  The  change  here  occurs  at  6  =  12  and  14,  so 
that  graphs  again  intersect.  The  second  crest  is  often  uncertain  and  the 
trough  shifts  as  before,  particularly  at  6  =  12,  14,  16  cm.  The  first  crest 
(C  =  0.1)  dominates  again  and  is  steady. 

Finally,  figure  242,  for  6  =  18,  20,  22,  24,  26,  28  cm.,  the  graphs  are  more 
nearly  of  the  same  kind,  except  that  for  5  =  26,  28,  changes  of  form  with  the 
resulting  intersections  occur.  In  other  respects  the  remarks  already  made 
apply. 


PROBE  AND  THE  INTERFEROMETER  U-GAGE 


133 


The  %s-graphs  are  given  in  figure  243,  and  they  are  taken  from  the  pre¬ 
ceding  figure  for  constant  C=o.i  (crest);  C  =  0.6  (trough);  and  C=i.i  (crest 
nearly).  The  first  of  these  is  definite  and  we  observe  (x  =  5+ 1). 

5=o  9  18  25  29  cm. 

trough  crest  trough  crest  trough 

The  distance  apart  of  crest  and  trough  diminishes  as  do  their  respective 
amplitudes  when  5  increases. 

The  other  two  graphs  (C= 0.6  and  1.1  microfarads)  suffer  from  lack  of 
definiteness,  though  they  in  general  corroborate  the  preceding.  The  humps 
between  *=12  and  13  cm.  are  unexpected,  but  they  need  not  be  errors  of 
adjustment. 

It  is  seen  that  the  troughs  in  this  essentially  salient  plate  pin-hole  are 
usually  positive,  though  negative  5  occurs  for  5  =  12,  14,  16,  18  cm.  The 
crests  are  strongly  positive.  Hence,  the  excess  pressures  occur  on  the  side 
of  the  plate  pin-hole  (burr  side)  in  the  direction  in  which  the  puncturing 
needle  advanced,  even  though  the  endeavor  was  made  to  ream  these  holes 
cylindric.  The  residual  burr  side  is  here  positive,  nevertheless. 

85.  The  same.  Plate  pin-hole  reversed — To  test  this  it  was,  however, 
necessary  to  reverse  the  pin-hole  plate.  This  was  done  by  cutting  the  quill- 
tube  at  2  cm.  from  the  plate,  reversing  the  short  (pin-hole)  end  and  resolder¬ 
ing  it  to  its  quill-tube.  The  puncture  was  now  burred  toward  the  outside, 
so  that  the  U-gage  should  register  pressure  deficiency. 

The  sC-graphs  for  the  reversed-plate  pin-hole  are  given  in  figure  244. 
There  is  an  obvious  tendency  of  these  to  be  mirror  images  of  the  preceding 
set  (figs.  240,  etc.)  in  the  initial  parts  of  the  graphs,  when  the  negative  crest 
at  C= 0.1  microfarad  is  intense  (as,  for  instance,  when  #=7,  9,  11,  13  cm.); 
but  with  ^  =  15  a  new  departure  is  made,  with  the  chief  crest  at  C  —  0.2.  So 
also  the  final  tendency  of  these  graphs  to  become  positive  is  not  in  symmetry 
with  the  preceding  set  (fig.  240).  The  periodicity  in  figure  244  is  as  a  rule 
much  more  crowded. 

Because  of  this,  the  sx-graphs,  figure  245,  were  taken  at  C  =  o.i  micro¬ 
farad  and  1.0  microfarad  only.  The  negative  troughs  at  x  =  g  (5  =  8  cm.) 
are  both  marked;  the  negative  crests  at  x  =  $  (5  =  4)  and  x  =  i6  (5  =  15)  are 
suggested.  The  phenomena  as  a  whole  are  too  complicated  for  discussion 
apart  from  the  graphs. 

86.  The  same.  Further  experiments — As  the  quill-tubes,  anterior  and 
posterior,  were  slightly  different  in  diameter  (0.3  cm.  and  0.35  cm.,  respec¬ 
tively)  in  the  last  case,  a  test  with  tubes  of  identical  bore  (0.35  cm.)  was 
repeated.  The  pin-hole  plate  was  of  thin  aluminum  foil  in  this  case  and 
0.035  in  diameter.  It  is  called  salient  if  pierced  from  the  outside,  so  that  any 
burr  would  fall  within  the  quill-tube  probe.  The  connection  with  the  U-gage 
was  at  least  75  cm.  long,  with  a  glass  quill  30  cm. 

The  results  for  the  salient  case  are  given  in  figures  246  and  247.  The 


134 


ACOUSTIC  EXPERIMENTS  WITH  THE  PIN-HOLE 


pin-hole  is  less  sensitive  and  the  graphs  simpler;  but  as  a  whole  they  conform 
to  the  corresponding  behavior  of  the  copper-plate  pin-hole.  They  need  not, 
therefore,  be  referred  to  in  detail. 

In  figure  248,  I  have  constructed  the  s#-graph  for  the  main  crest  C  =  o.i 
microfarad  and  for  the  far  crest  near  C— 1.0  microfarad.  The  sinuous  fluct¬ 
uations  are  peculiar,  but  there  is  no  reason  for  dismissing  them.  The  case 
of  C— 1.0  is  particularly  anomalous.  When,  C= 0.1,  the  troughs  and  crests 
occur  in  succession  at  6  =  0,  9,  18,  28  cm.,  with  a  low  value  at  5  =  32  cm. 
While  the  crests  graphs  are  nearly  all  positive,  the  troughs  graphs  (s%),  also 
given  by  the  figure,  are  prevailingly  negative,  with  a  succession  of  the  promi¬ 


nent  negative  crests  and  troughs  at  6  =  5,  12.5,  22  cm.  approximately,  the 
tendency  being  to  fall  between  the  troughs  in  their  x  position;  yet  a  curious 
resemblance  between  the  cases  C= 0.7  and  1.0  microfarad  is  noticeable. 

Finally,  figure  249  gives  a  summary  of  the  sC-graphs  for  the  reversed 
position  of  the  almninmn -plate  pin-hole.  The  curves  are  very  complicated, 
but  in  the  main  resemble  the  results  for  the  reversed  copper-plate  pin-hole. 
Crests  of  the  salient  cases  are  changed  to  troughs  for  the  reentrant  case,  but 
with  a  marked  tendency  of  all  crests  and  troughs  to  shift  in  their  C  position 
periodically.  The  strong  C=o.i  trough,  for  instance,  for  #  =  3  is  now  given 
by  a  crest  at  C= 0.05  and  a  trough  at  0.3  microfarad. 

The  5%-graphs,  figure  250,  in  this  case  are  taken  for  C=o.i  and  1.0  (crests) 
and  for  C=o.6  (troughs).  The  result  at  C=i.o,  with  a  crest  at  5  =  2  and  18 
cm.  and  a  trough  at  5  =  12  cm.,  is  the  more  definite.  The  graph  for  troughs 


PROBE  AND  THE  INTERFEROMETER  U-GAGE 


135 


tends  to  reverse  the  case  for  crests.  The  hump  in  the  C=o.i  graph  is  un¬ 
expected. 

If,  now,  we  compare  the  plate  pin-hole  with  the  much  more  sensitive 
conical  glass  pin-hole  probe,  we  reach  the  anomalous  result  that  the  burr  side 
of  the  former  (the  side  opposite  to  the  one  first  pierced  by  the  needle)  and 
the  reentrant  side  of  the  cone  correspond.  If  the  U-gage  is  on  this  side  it 
will  register  pressure.  If  the  pin-holes  are  reversed,  the  registry  is  negative, 
or  pressure  deficiency.  Modification  of  the  steadiness  of  the  jet  through 
the  pin-hole  by  its  edges  in  some  way  seems  alone  left  to  account  for  this. 


87.  Salient  glass  pin-hole  with  anterior  quills— The  sensitive  glass  pin¬ 
hole  g  in  the  insert  of  figure  251  is  to  be  provided  with  the  anterior  quill- 
tube  gc,  of  length  8  =  x — 1,  the  mouth  being  1  cm.  from  the  bottom  of  the 
pipe  p.  The  rear  tube  bg  is  wide  and  long  (75  cm.)  connecting  at  the  far 
end  with  the  U-gage.  The  experiments  are  thus  an  inversion  of  the  set  in 
figures  233  and  237.  Since  bg  is  salient  and  gc  reentrant,  one  would  expect  a 
diminished  effect  in  5,  as  compared  with  bg  alone  under  like  circumstances. 
The  reverse  is  emphatically  the  case,  as  the  nodal  intensity  of  the  highest 
crest  is  over  eight  times  that  of  the  lowest  trough,  both  obtained  by  anterior 
quill-tube  additions.  The  pipe  p  was  29  cm.  long  and  all  vibrations  in  tune, 
as  heretofore. 

The  Cs-graphs  in  figures  251  to  253  show  a  chief  crest  at  about  (7  =  0.12 
microfarad.  There  is  a  subsidiary  one  near  C—  0.25  microfarad  (not  examined 
in  detail)  and  a  final  one  beyond  C— 1.0  microfarad.  For  short-tube  additions 
(5  =  2  to  6  cm.)  there  is  very  little  difference.  Hence,  though  the  pin-hole 


10 


136 


ACOUSTIC  EXPERIMENTS  WITH  THE  PIN-HOLE 


cone  was  surrounded  by  a  small  perforated  cylinder  of  cork  to  obtain  a  plane 
bottom  for  eg ,  this  seemed  to  be  a  useless  improvement.  Beyond  x  =  g  cm., 
however,  the  graphs  rise  and  then  fall  with  great  rapidity,  and  this  is  also 
true  again  beyond  x  =  2$  cm. 

The  5^-graphs  are  given  in  figure  254,  taken  at  C  =  o.i  and  C=  1.0  (crests) 
and  at  C  =  o.6  microfarad  (troughs),  remembering  that  the  troughs  fluctuate 
in  their  C  positions.  The  graph  for  C  =  o.i  microfarad  is  very  definite  and 
the  maxima  almost  cusplike.  The  graphs  for  the  C— 1.0  crest  and  the  trough 
graph  happen  to  be  nearly  coincident,  and  they  corroborate  the  high  graph 


in  a  general  way.  The  distribution  of  maxima  in  minima  is  as  follows  (5  = 
x  —  1  being  the  quill-tube  length  added) : 


Crest . 5  =  n  -  28  cm. 

Trough . .  5=22  - 


the  maxima  decreasing  rapidly  in  intensity  and  becoming  more  crowded  as 
5  increases.  The  relation  of  the  data  for  5  is  again,  as  1 ,  2 ,  and  a  very  scant  3 , 
attributable  to  viscosity. 

The  position  of  the  main  cusp  and  trough  in  these  experiments  is  higher 
than  heretofore,  when  they  were  found  below  x  =  io  and  20,  respectively. 
This  may  result  from  unavoidable  progressive  differences  in  tuning,  but  it 
is  to  be  noticed. 

Comparing  figures  254  and  237,  we  see  that  the  enhancement  due  to 
anterior  quills  is  of  the  same  order  and  sign  as  the  pin-hole  effect  (±5),  whether 
the  pin-hole  is  salient  or  reentrant. 

To  corroborate  the  xs  results  of  figure  254,  direct  experiments  to  trace  the 


PROBE  AND  THE  INTERFEROMETER  U-GAGE 


137 


graphs  at  the  crest  value  C  =  0.12  microfarad,  were  made.  Two  examples  of 
these  are  given  in  figures  255  and  256,  curve  a  in  terms  of  the  quill-tube  length 
5  =  *  —  1  added.  As  the  excursions  are  too  large  for  the  ocular  micrometer, 
the  slide  micrometer  was  used,  wherefore  (r)  =  10  (5)  about,  is  the  expanded 
scale-unit  of  the  ordinates.  The  two  graphs  are  identical  in  their  features. 
They  differ  somewhat  from  each  other  in  corresponding  ordinates  (nodal 
pressures),  owing  to  the  unavoidable  changes  of  pitch  during  the  long  inter¬ 
vals  of  observation.  The  chief  maximum  at  a  mean  length  of  6  =  12  cm.  is 
now,  curiously  enough,  edentate.  It  is  again  to  be  ascribed  to  slight  differences 
in  pitch,  or  inadequate  tuning  of  the  organ-pipe  with  reference  to  the  spring- 


break,  to  which  the  sharp  cusp  in  figure  254  is  very  sensitive.  Apart  from 
this  the  chief  crests  and  troughs  in  figures  255  and  256  may  be  placed  at 

Crest  8 .  12  -  29  cm. 

Trough  5 . — —  24  — • — • 

somewhat  higher  even  than  figure  254.  The  edentate  feature  has  frequently 
occurred  in  the  graphs  obtained  heretofore. 

Subsequently,  by  a  side  adjustment  shown  in  the  next  paragraph,  this 
work  was  partially  repeated,  with  results  summarized  in  figure  256,  curve  b. 
The  organ-pipe  here  was  scrupulously  tuned.  As  a  consequence,  the  graph  is 
again  cusplike  (as  in  fig.  254)  and  its  amplitude  (5  =  1  or)  fully  equal  to  that 
in  the  earlier  figure.  Hence,  the  edentures  obtained  are  actually  introduced 
by  an  inadequate  pitch  adjustment.  The  chief  maximum  is  now  at  8  =  11  cm., 
as  in  figure  254. 

88.  Rear  quill-tubes  variable — -In  the  preceding  series  of  experiments 
the  quill-tube  connection  between  pin-hole  probe  and  U-gage  was  very  long 


138 


ACOUSTIC  EXPERIMENTS  WITH  THE  PIN-HOLE 


(75  cm.  and  over)  and  left  constant  in  length,  while  the  anterior  quills  between 
the  pin-hole  and  the  open  end  in  the  pipe  p  were  varied  in  length.  In  the 
present  series  the  case  is  to  be  reversed.  To  make  this  possible,  the  apparatus 
was  modified  as  shown  in  the  insert,  figure  257,  where  the  quill-tube  connectors 
be  with  the  pin-hole  probe  at  g  enter  the  sides  of  p  at  about  1  cm.  from  the 
bottom.  The  closed  shank  of  the  U-gage  is  at  the  mouth  of  b.  One  is  thus 
enabled  to  reduce  the  length  bg  =  8'  to  about  5  cm.  with  a  little  uncertainty, 
owing  to  the  conical  form  of  g.  The  length  gc  =  8  may  of  course  also  be  varied. 
The  slide  micrometer  (10 r=s)  was  used,  as  before. 

In  all  these  experiments  there  are  necessarily  two  pin-hole  probes,  bg 
and  gc}  counteracting  each  other.  The  efficiency  of  one  will  thus  be  a  maxi¬ 


mum  when  the  other  is  at  a  minimum.  It  was,  therefore,  first  necessary  to 
make  the  survey  (r,  8)  of  the  effect  of  varying  8  when  8 '  is  constant  and  very 
long  (75  cm.).  These  results  are  given  in  figure  257  as  obtained  with  a  care¬ 
fully  tuned  pipe  p.  The  graph  is  remarkably  regular,  with  the  cardinal  points. 


Crests:  8 .  10  -  29  — —  46  cm. 

Troughs:  8 . .  20  -  39  -  cm. 


Double  amplitude  .  .2a  =  51  —  16  =  35  40  —  17  =  23  31—18  =  13 

so  far  as  they  can  be  located.  The  amplitude  falls  off  slowly  with  5,  as  usual, 
and  the  wave-length  decreases.  Troughs  lie  between  the  crests  and  vice 
versa,  very  nearly.  It  is  particularly  noticeable  that  crests  fall  more  than 
troughs  rise,  these  being  nearly  stationary. 

If  the  successive  double  amplitudes  (rcrest—rtrough  =  2a)  be  coordinated 
with  the  crests  8,  the  graph,  figure  257,  is  nearly  linear  and  2a  —  o  should  occur 


PROBE  AND  THE  INTERFEROMETER  U-GAGE 


139 


at  5  =  68  cm.,  but  the  effect  is  more  liable  to  be  asymptotic.  The  relation 
is  nearly  2 a  =  41  —0.68.  The  subject  will  be  resumed  below  (fig.  260). 

The  quill-tube  gc  was  now  kept  at  the  length  5  =  10  cm.,  corresponding  to 
the  maximum  in  figure  257,  while  bg  was  varied  in  length  from  5' =  5  cm.  to 
59  cm.  The  results  of  the  survey,  given  in  figure  258,  are  quite  peculiar  and 
decisive.  In  the  first  place,  the  crests  in  5'  (fig.  258)  coincide  in  quill-tube 
length  with  troughs  in  5  (fig.  257).  This  ceases  to  be  fully  the  case  when  5 
exceeds  about  45  cm.,  but  one  can  hardly  expect  that  the  joining  together  of 
these  long  lengths  of  quill-tube  can  be  made  without  some  shift.  Moreover, 
there  is  the  cone  at  g  which  introduces  uncertainty  at  the  abutting  5,  5' 
lengths. 

In  the  second  place,  the  first  trough  in  figure  258  is  very  sharp  and  the 
final  crest  apparently  edentate.  This  indicates  a  shift  of  pitch,  probably, 
so  that  the  pipe  p  was  no  longer  adequately  tuned.  The  second  and  third 
crests,  as  suggested  in  figure  258,  are  astonishingly  truncated  over  a  wide  5' 
interval.  The  fringe  position  in  these  experiments,  moreover,  is  not  quite 
steady,  but  fluctuating  over  a  small  interval,  to  be  associated  with  variation 
in  the  action  of  the  spring-break.  Granting  this,  the  crests  and  troughs  may 
be  thus  placed: 


Troughs:  5' .  11  — —  30  -  48  cm. 

Crests:  5' . .  17  -  37  -  57  cm. 


where  the  appearance  is  of  troughs  falling  midway  between  crests.  The  close 
resemblance  of  this  arrangement  with  the  preceding  (5)  is  striking;  but  now 
the  crests  are  nearly  stationary,  with  the  troughs  rising  rapidly. 

The  high  acoustic  pressures  registered  here  are  to  be  noticed.  The  first 
crest  gives  r  —  0.053  cm.,  which  corresponds  to  more  than  a  third  of  a  milli¬ 
meter  of  mercury.  That  such  pressures  are  producible  by  vibration  in  long 
quill-tubes  is  quite  unexpected. 

If,  instead  of  placing  the  5  quill  at  a  crest-length  (5  =  10  cm.),  it  had  been 
placed  at  a  trough-length  (8  =  20  cm.),  this  should  merely  drop  the  graph 
toward  the  abscissa;  and  the  troughs  might  even  become  negative  if  8' 
were  not  the  dominating  pin-hole  probe.  The  results  actually  obtained  (fig. 
259)  show  more  than  this,  for  the  curve  has  appreciably  changed  form.  The 
troughs  are  still  sharp,  but  the  truncated  crests  are  less  interpretable  than  in 
figure  258,  although  the  preceding  distribution  of  crests  and  troughs  may  be 
accepted.  The  tendency  at  the  beginning  toward  a  sawtooth  graph  is  unmis¬ 
takable.  Crests  fall;  troughs  rise.  Clearly  the  pin-hole  probe  8'  dominates, 
so  that  the  graph  is  never  in  negative  regions.  One  may  regard  8'  as  measuring 
the  node  at  the  pin-hole  in  5  and  that  the  mean  value  of  this  never  quite 
vanishes.  The  pin-hole  acts  as  an  embouchure  to  the  quill  bg  while  vibration 
in  gc  is  actuated  by  the  pipe  p.  The  excess  pressure  is  on  the  side  of  the  shaft 
of  the  musical  instrument  actuated  by  the  pin-hole. 

Later  the  graph,  figure  259,  was  prolonged  as  far  as  8'  =  86  cm.,  a  part  of 


140 


ACOUSTIC  EXPERIMENTS  WITH  THE  PIN-HOLE 


which  is  raised  in  the  diagram.  The  data  to  be  obtained  from  these  experi¬ 
ments  are  summarized  in  the  following  table: 


5 

Sharp 

crests 

S' 

Displ. 

r 

Sharp 

troughs 

S' 

Displ. 

r 

Double 

amplitude 

2  a  =  A  r 

Mean 

S' 

20 

13 

31 

II 

6 

25 

12 

(trough) 

33 

25 

29 

6 

19 

31 

5i 

26 

47 

12 

14 

49 

70 

21 

64 

10 

II 

67 

* 

81 

9 

r  T 1 

The  sharp-edged  crests  and  troughs  of  the  saw-tooth  waves  are  meant.  Their 
average  distance  apart  is  about  18  cm,  and  there  is  no  marked  diminution  of 
wave-length  with  increasing  tube-length  8'  here.  The  double  amplitudes 
decrease  as  shown  in  figure  262,  slowly  and  retardedly  (the  first  three,  how¬ 
ever,  linearly)  so  as  to  reach  an  asymptote  somewhat  below  Ar  =  2a  =  io. 
This  should  be  a  steady  fluctuation,  as  the  saw-tooth  shape  becomes  less 
abrupt,  more  smoothly  sinuous,  beyond  1  meter  of  quill-tube  length,  prob¬ 
ably.  There  is  here  no  evidence  that  the  sinuous  curve  will  eventually 
straighten  out.  It  is  again  astonishing  that  these  thin  tubes  (diameter  0.35 
cm.)  can  sustain  such  prolonged  waves  for  so  great  a  distance,  in  spite  of  the 
viscosity  of  air.  The  2 a  values,  denoting  pressures,  are  proportional  to  energy 
values  per  cubic  centimeter. 

We  may  now  summarize  the  results  of  the  last  paragraphs,  as  obtained 
with  two  identical  collinear  counteracting  quill-pipes  (diameter  0.35  cm.), 
one  of  which  may  eventually  be  nearly  a  meter  long,  separated  by  a  pin¬ 
hole  somewhere  between  the  ends  (see  fig.  257,  etc.).  We  note  that  coor¬ 
dinated  acoustic  oscillation  occurs  in  both  pipes  throughout  the  long  distances. 

If  the  pin-hole  were  in  a  plate  and  the  edges  identical  on  both  sides,  and  if, 
furthermore,  the  pipes,  8'  and  8,  were  equally  long,  it  is  difficult  to  believe 
that  any  differentiation  of  the  two  sides  could  occur.  If  the  lengths  8'  and  8 
are  unequal,  that  corresponding  to  the  length  of  any  harmonic  might  be 
supposed  to  concentrate  the  stronger  node  at  the  pin-hole  and  that  the  pres¬ 
sure  excess  would  be  on  that  side  toward  which  the  stronger  node  pushes, 
postulating  compression  to  be  more  effective  in  the  transfer  of  air  through 
the  pin-hole  than  the  following  dilatation  at  the  node.  The  case  is  conceived 
to  approximate  to  the  pull  of  a  vibrating  string  on  its  abutments,  without 
any  corresponding  push.  The  abutments  are  drawn  toward  each  other 
twice  in  a  period.  This  case  was  examined  for  pin-holes,  in  §  5 1  et  seq. ;  but  it 
suggests  no  reason  for  the  reversal  of  pressure  difference  when  the  identically 
sided  pin-hole  is  reversed  and  is  thus  inadmissible. 

89.  Further  experiments,  8  =  10  cm.,  8'  variable — It  seemed  worth 
while  to  repeat  the  interesting  series  (fig.  258),  where  8  is  at  a  crest-length, 
in  such  a  way  as  to  prolong  the  curve  further.  This  has  been  done  in  figure 
261,  where  8'  eventually  reaches  93  cm.  The  last  part  of  the  graph  has  been 


PROBE  AND  THE  INTERFEROMETER  U-GAGE 


141 


dropped  io  scale-parts  in  r,  as  it  goes  beyond  the  figure.  There  is  no  essential 
difference  between  figure  261  and  figure  258,  apart  from  the  capriciousness  of 
intonation.  The  crests  are  again  almost  stationary  in  their  r  values,  while  the 
troughs  rise  rapidly  with  h'  to  a  limit.  Their  position  is 

$'  =  n  30  47  65  85  cm. 

so  that  the  wave-length  here  can  not  be  said  to  decrease;  rather  the  reverse. 
The  truncated  crests  which  eventually  tend  to  become  sinuous  can  not  be 
similarly  defined  as  to  their  5'  position.  We  may,  however,  construct  the 


r  difference  of  crest  and  the  ensuing  trough  and  assume  this  to  hold  for  their 
mean  5'  position.  Thus  the  amplitudes  2a  =  rcrest—rtrough  are  obtained. 

(Mean)  5'=  8  26  44  61  80  cm. 

2a  =  36  21  15  15  12 

These  values  are  also  given  in  figure  262.  At  the  outset  the  2 a  for  the  crest- 
graph  is  much  in  excess  of  the  2 a  for  the  trough-graph,  as  one  might  expect; 
but  after  a  quill-pipe  length  of  5'  =  30  cm.,  the  tendency  of  both  is  not  so 
very  different,  and  they  indicate  an  eventual  oscillation  of  r  over  an  amplitude 
of  about  2a  =  rcrest-rtrough  =  io.  It  is  probable  that  figure  260  would 
take  the  same  course  if  prolonged. 

90.  Pin-holes  varied — By  far  the  most  efficient  probe  thus  far  has 
been  the  quill-tube  cone,  yielding  as  much  as  s  =  600  acoustic  pressure 
with  the  given  telephone-exciter  or  sound  intensity,  or  over  four  times  as 
much  as  the  above  plate  pin-holes  (caet.  par.).  The  glass  probe  is  essentially 


142 


ACOUSTIC  EXPERIMENTS  WITH  THE  PIN-HOLE 


a  hollow  truncated  cone,  so  that  the  oscillating  air-current  strikes  a  sharp 
circular  edge.  Pressure  is  observed  in  the  interior  of  the  cone,  and  dilation 
(relatively)  on  the  outside.  If  we  imagined  an  air-current  toward  the  inside 
were  converted  into  pressure,  whereas  an  outward  jetlike  current  were  not, 
at  least  in  the  same  degree,  we  should  simulate  the  action  of  the  probe.  Being 
an  embouchure,  the  need  of  an  optimum  diameter  of  pin-hole  is  implied, 
but  it  will  presently  appear  that  the  need  of  a  sharp  edge  is  even  more  imper¬ 
ative,  and  it  seems  natural  that  there  should  be  more  vorticity  in  one  side 
of  the  pin-hole  than  on  the  other. 

In  many  respects,  however,  the  plate  embouchure  is  more  interesting, 
for  here  one  can  modify  the  bore  and  edge  character  of  the  pin-hole,  which 


in  case  of  the  glass  quill-tube  cone  has  to  be  ground  sharp  to  size.  It  has, 
therefore,  been  necessary  to  give  further  attention  to  the  simple  plate  device 
(see  g,  fig.  265)  and  the  more  important  results  are  recorded  in  figures  263 
and  264,  the  abscissas  merely  indicating  the  consecutive  experiments.  It 
was  further  found  that  the  direction  of  the  initial  current  in  the  telephone 
made  considerable  difference.  Hence,  the  latter  is  provided  with  a  switch 
and  its  first  position  (I)  is  indicated  by  open  circles,  the  opposite  position  (II) 
by  black  circles.  It  was  thought  that  the  difference  was  merely  an  expression 
of  less  efficiency  of  the  telephone  in  the  former  case;  but  this  is  not  true,  as  so 
many  of  the  black  circles  are  negative  in  5.  In  each  case,  the  plate  pin-hole 
probe  (plate  on  a  quill-tube  2  cm.  long,  0.35  cm.  in  diameter)  was  tested  both 
in  the  salient  (5)  and  the  reentrant  (r)  position  in  relation  to  the  U-gage  (see 
insert,  fig.  265).  Diameters  of  the  pin-holes  pricked  by  a  fine  cambric  needle 


PROBE  AND  THE  INTERFEROMETER  U-GAGE 


143 


are  also  given.  The  very  fine  pin-holes  (diameter  0.02  cm.)  are  unfortunately 
too  slow  for  convenient  use.  Finally,  the  thickness  0  of  the  foil  (plate)  in  which 
the  pin-hole  is  pricked  from  the  outside  of  the  tube  is  entered,  making  the 
record  complete.  The  insert,  figure  265,  gives  the  adjustment  of  quill-tube 
be  with  pin-hole  at  g  to  the  pipe  p  actuated  by  the  telephone  at  T,  and  the 
interferometer  U-gage.  Pipe  spring-break  of  the  circuit  and  electric  oscilla¬ 
tion  are  in  tune  with  the  relation  of  Ug  (6.5  cm.)  to  gc  (10  cm.)  corresponding 
to  a  maximum  fringe  displacement  5.  At  the  beginning  of  the  record  (fig. 
263a)  is  the  above  aluminum  pin-hole.  After  being  scratched  on  the  inside 
of  the  tube  to  close  the  burr,  it  becomes  strongly  negative,  though  salient. 
Punctured  a  second  time,  it  is  again  positive,  and  thereafter  soon  loses  its 
efficiency.  Nos.  2  and  3  are  similar  pin-holes  of  vaiying  size.  The  diameter 
effect  within  its  range  is  not  definite,  showing  that  some  other  factor  deter¬ 
mines  its  behavior.  Salient  in  position  I,  it  is  as  a  rule  strongly  positive  and 
reentrant  in  position  II  more  strongly  negative;  but  there  are  many  exceptions. 

Nos.  1,  o,  4,  7  were  punctured  in  much  thinner  aluminum  foil,  and  the 
favorable  effect  of  this  is  at  once  apparent  in  the  improved  efficiency  (larger  s) 
of  the  probes.  In  other  respects  the  remarks  already  made  apply.  Nos.  4 
and  7  were  constructed  with  greater  skill. 

These  experiments  at  once  indicate  the  nature  of  the  missing  factor, 
for,  heretofore,  the  thickness  of  the  foil  has  been  ignored.  It  is  clearly  of  as 
great  importance  as  the  diameter  of  pin-hole. 

Following  this  suggestion,  I  next  pricked  pin-holes  in  mica  plate,  split 
as  thin  as  admissible  and  much  below  0.0 1  mm.  The  results  in  figure  264 
show  the  enormously  increased  efficiency  obtained,  ordinates  being  even  five 
times  as  large  as  those  in  the  original  thick  foil.  No.  5  was  only  examined 
for  diameter  0.02  cm.  In  No.  6  there  is  but  little  difference  between  the 
first  two  diameters.  In  puncturing  the  third,  the  hole  was  accidentally 
frayed  to  about  twice  the  area  wanted  and  beyond  the  admissible  range. 
Hence,  the  low  efficiency,  s. 

There  is,  however,  always  difficulty  in  successfully  enlarging  the  pin-hole. 
For  instance,  in  No.  8  the  original  efficiency  (diameter  0.02)  is  very  large, 
particularly  in  the  negative,  but  the  fringe  displacement  is  annoyingly 
slow.  On  enlarging  the  bore  to  0.035  and  0.042  cm.,  its  efficiency  is  lost. 
No.  9  is  another  peculiar  case  in  which  the  fine  pin-hole  is  negative  in  the 
salient  and  positive  in  the  reentrant  position,  a  rare  inversion  of  the  usual 
occurrence. 

The  final  graph  shows  the  corresponding  behavior  of  an  efficient  glass 
pin-hole,  one  of  the  best.  The  fine-hole  mica  probe  is  thus  of  the  same  order 
of  excellence. 

If  we  take  the  highest  of  the  5  values,  corresponding  to  any  thickness 
of  foil  0,  and  plot  5  against  0,  we  get  a  graph  (fig.  266)  of  hyperbolic  contour, 
giving  a  mean  estimate  of  the  results  obtained.  The  smallest  manageable 
thickness  of  plate  is  thus  of  cardinal  importance;  in  other  words,  the  pin¬ 
hole  should  be  a  sharp  circle,  and  anything  of  the  nature  of  a  capillary 


144 


ACOUSTIC  EXPERIMENTS  WITH  THE  PIN-HOLE 


tube,  however  short,  is  detrimental.  The  viscosity  of  air  is  here  liable  to 
ruin  the  experiment. 

And  yet  the  two  sides  of  the  pin-hole  behave  quite  differently  to  the 
current  of  air  propelled  through  it  by  the  alternating  nodal  pressure.  Hence, 
the  production  of  vortices  at  the  pin-hole  by  the  acoustic  pressures  seems 
alone  to  be  in  keeping  with  the  observed  results.  The  oscillating  air-columns 
in  contact  at  the  pin-hole  are  successively  shooting  vortices  into  each  other 
and  the  pressure  difference  results  because,  owing  to  the  structure  of  the 
pin-hole  in  question,  one  of  the  air-columns  does  this  more  efficiently  than 
the  other.  One  should  expect  the  pressure  to  be  largest  on  the  side  of  less 
vorticity ;  for  it  is  here  that  the  energy  of  the  discharge  current  across  the  pin¬ 
hole  has  been  in  greater 
measure  converted  into  vortex 
motion  within  the  pin-hole 
probe. 

Though  a  large  number  of 
further  experiments  were 
made,  the  results  at  first 
showed  no  improvement,  and 
the  success  obtained  was  al¬ 
ways  a  matter  of  chance. 
Typical  examples  are  given  in 
figure  267  in  case  of  probes 
Nos.  21  to  26,  all  with  holes 
0.02  cm.  in  diameter.  In  the 
former  (21),  paired  holes  were 
also  tested,  insuring  a  shorter 
interval  of  displacement;  but 
as  a  rule  the  second  hole  is 
liable  to  decrease  the  sensi¬ 
tivity,  as  only  in  rare  cases 
will  two  equally  good  holes  be  pierced.  A  distinct  advance  of  technique, 
however,  is  attested  by  the  probes  Nos.  27  to  35,  in  which  the  piercing  needle 
passed  through  the  mica  into  a  small  stick  of  wood  placed  immediately 
behind  the  mica  and  receiving  the  full  stress  of  the  puncture.  The  grain 
should  be  parallel  to  the  needle.  The  perfection  of  contact  of  wood  support 
and  mica  plate  insures  the  best  results  (No.  27). 

The  salient  position  of  probe  punctured  from  the  outside  is  always  positive 
(pressure  in  gage)  and  the  reentrant  position  negative;  moreover,  the  effect 
of  positions  I  and  II  of  the  telephone-switch  is  generally,  though  not  uniformly, 
consistent.  Nevertheless,  an  initial  thrust  of  telephone-impulse  in  the  salient 
position  and  a  pull  in  the  reentrant  position  are  seen,  as  a  rule,  to  be  equiva¬ 
lent  in  effectiveness.  If  the  thrust  produces  the  greater  positive  value,  the 
pull  will  follow  with  the  greater  negative  value.  Dependence  of  sensitivity 
on  size  of  hole  in  relation  to  pitch  could  not  be  found.  In  figure  268,  the  time 


PROBE  AND  THE  INTERFEROMETER  U-GAGE 


145 


needed  to  obtain  the  full  displacement  in  case  of  holes  0.02  cm.  in  diameter 
is  graphically  given  by  noting  the  seconds  elapsed  during  successive  displace¬ 
ments  of  As  =  100.  After  the  first  minute,  at  least  10  per  cent  is  added  to  the 
displacement  and  not  more  than  70  per  cent  of  its  full  value  is  observed 
dining  the  first  half  minute.  In  this  respect  the  glass  pin-hole  cone,  which 
admits  of  a  larger  aperture  and  is  practically  instantaneous  in  its  response, 
is  preferable,  even  if  the  mica-plate  pin-hole  often  shows  the  superior  sensi¬ 
tivity  of  No.  27,  for  instance.  Finally,  mica  punched  from  without  is  almost 
invariably  positive  and  corresponds,  therefore,  to  the  salient  cone. 


CHAPTER  V 


MISCELLANEOUS  EXPERIMENTS  WITH  THE  INTERFEROMETER  U-GAGE 

Pressure  Phenomena  of  the  Electric  Wind 

91.  Apparatus — The  spectacular  group  of  experiments,  which  we  use 
to  perform  once  a  year,  seem  but  rarely  to  have  come  to  any  useful  maturity. 
I  can  recall  only  the  electronic  measurements  of  Professor  Chattock.  Having 
the  apparatus  at  hand,  it  seemed  interesting  to  look  at  them  in  detail,  and  in 
the  attached  figures  I  will  summarize  the  main  results. 

The  simple  apparatus  as  originally  used  (fig.  269,  insert)  consisted  of 


the  two  brass  posts,  P,  P',  usually  8  cm.  apart  and  fixed  in  the  hard  (or  soft) 
rubber  base  B.  T  supported  by  P  is  a  small  thimble  of  brass  perforated 
by  the  slender  tube  U,  which  leads  to  the  interferometer  U-gage.  The  post 
P'  carries  the  darning-needle  n  coaxially  with  U,  and  both  n  and  U  fit  snugly, 
so  that  they  may  be  slid  to  different  distances,  x,  apart.  P  and  P'  are  in 
contact  with  the  poles  of  a  small  Wimshurst  machine,  capable  of  delivering 
half-inch  sparks.  The  latter  was  usually  turned  by  hand  near  a  clock  beating 
quarter  seconds,  and  the  speed  of  rotation  of  six  turns  (sometimes  three 
turns)  per  second  for  each  plate  was  easily  maintained. 

92.  Needle  electrode — The  group  of  curves,  a,  refers  to  a  hard-rubber 
base  with  posts,  P,  P',  8  cm.  apart.  Irregularities  are  referable  to  freakish 

146 


PIN-HOLE  PROBE  AND  THE  INTERFEROMETER  U-GAGE 


147 


action  of  the  machine,  quite  apart  from  rotation;  but  it  is  noticeable  that  the 
pressures  (s,  approximately  in  io"6  atmosphere)  are  roughly  double  for  6  rot./ 
sec.  as  compared  with  3  rot. /sec.  I  was  disappointed  at  the  relatively  low 
pressures  here  in  evidence,  and  therefore  scraped  and  boiled  the  hard-rubber 
base  in  dilute  acid  for  greater  insulation.  The  resulting  graph  actually 
shows  reduced  sensitivity  and  now  suggests  a  maximum.  In  curve  b  a  soft- 
rubber  base  was  tested.  The  graph  is  smoother,  with  a  very  definite  crest, 
but  no  better  in  s,  and  finally,  the  graph  cona  cylindrical  hard-rubber  base 
is  no  advance  on  the  others. 

Improved  conditions  appear  with  graph  d,  referring  to  posts  P,  Pr  but 
4.5  cm.  apart.  Whether  one  or  three  sharp  needles  are  used  is  relatively 


immaterial;  but  this  graph  is  rapidly  accelerated  upward.  Close  inspection 
of  the  data  convinced  me  that  the  graph  essentially  consists  of  two  constitu¬ 
ents,  one  of  which  tends  to  a  low  crest  as  heretofore,  while  the  other  begins 
at  the  maximum  and  runs  with  great  rapidity  to  high  5,  while  the  needle 
projects  but  a  few  millimeters  beyond  the  post  P'.  When  the  needle-point 
retreats  just  within  the  post,  the  curve  drops  instantly  to  zero.  Sparks, 
or  sputtering,  is  equivalent  to  s  =  o. 

To  accentuate  this  result,  the  thimble  was  cut  down  (the  form  is  prac¬ 
tically  immaterial)  as  in  the  insert,  figure  270,  admitting  of  larger  x  between 
the  same  posts.  The  graphs  a  and  b  (for  a  somewhat  wider  x  space)  fully 
bear  out  the  surmise,  and  the  cusp  of  b  has  risen  to  nearly  four  times  the 
height  of  the  crests  in  a,  b,  c,  figure  269.  What  the  larger  x  insures  is  probably 
greater  axial  momentum  of  the  ionized  wind,  which  in  its  complete  form 


148 


ACOUSTIC  EXPERIMENTS  WITH  THE  PIN-HOLE 


must  be  a  ring-vortex  symmetrical  to  the  needle.  A  point  immediately 
in  front  of  a  surface  of  high  potential  gives  the  latter  a  longer  range  of  action. 
Eventually,  the  life  of  the  ions  and  their  space  density  would  be  in  question. 

The  position  of  charged  masses  (like  the  poles  of  the  electric  machine) 
must  materially  affect  the  form  of  the  graphs  by  deflecting  the  air-currents. 
Such  objectionable  features  are  to  be  scrupulously  removed  in  the  next 
section.  No  pressures  (s)  are  observed  until  the  charge  of  the  machine  exceeds 
a  certain  specific  threshold  or  ionizing  potential,  after  which  the  appropriate 
pressure  (5)  appears  at  once.  In  the  reverse  case,  pressure  (s)  vanishes  before 
the  machine  is  discharged.  The  greatest  difficulty  thus  far  has  been  the 
fluctuating  potential  of  the  machine,  due,  so  far  as  I  can  see,  to  casual  partial 
self-discharge  within. 


93.  Mucronate  electrode — Borrowing  a  term  from  the  botanists:  What 
is  needed,  therefore,  is  a  slightly  convex  electrode  E',  with  a  sharp  fixed 
needle-point  projecting  less  than  a  millimeter  from  its  center  (see  insert, 
fig.  271)  and  (convexities  toward  each  other)  facing  a  similar  but  unarmed 
electrode  E.  P ,  P'  as  before  are  4.5  cm.  apart. 

The  results  obtained  with  this  mucronate  electrode  (fig.  271)  are  astonish¬ 
ing,  for  the  curve  sweeps  aloft  in  some  cases  to  over  five  times  the  heights 
of  the  original  crests.  Thus  far  these  graphs  have  not  started  until  £  =  0.5 
cm.  is  passed.  They  are  peaked  at  the  upper  end,  and  soon  thereafter  drop 
from  the  sharp  crest  to  s  =  o.  They  imply  a  degree  of  sensitivity  that  makes 
interferometer  observation  difficult,  every  little  irregularity  of  the  Wimshurst 
being  magnified. 


PROBE  AND  THE  INTERFEROMETER  U-GAGE 


149 


To  increase  the  range  of  the  experiments,  it  was  necessary  to  place  the 
posts  P,  P'  further  apart.  This  was  done  on  the  same  base  by  a  metallic 
extension  carrying  P'  from  about  4  to  8  cm.  Results  so  obtained  are  given 
in  figure  272,  the  graph  b  having  an  improved  E  electrode.  The  presence  of 
the  massive  extension,  however,  probably  deflected  the  air-current;  hence, 
the  graphs  fall  off  rapidly  in  this  region. 

The  hard-rubber  base  with  posts  10  cm.  apart  was  therefore  substituted 


and  the  results  given  in  figure  273  worked  out.  These  fall  off  at  x  =  6  cm., 
which  is  the  position  of  one  of  the  poles  of  the  electric  machine.  In  case  of 
graph  b  the  mucronate  electrode  was  improved,  as  shown  in  the  insert. 
A  brass  rod  N  (5  mm.  in  diameter)  carries  the  sharp  needle-end  n  all  but 
embedded  in  its  end  with  the  point  just  projecting.  A  remarkable  increase  of 
sensitivity  is  thus  obtained,  owing  in  part  to  the  more  careful  polish  of  the 
slightly  convex  electrodes.  The  crest  almost  reaches  5  =  300,  but  the  descent 
is  still  irregular. 

It  was  therefore  necessary  in  the  next  experiments  to  place  the  poles 


150 


ACOUSTIC  EXPERIMENTS  WITH  THE  PIN-HOLE 


of  the  electric  machine  quite  beyond  the  posts  P,  P' ;  for  it  is  only  when 
the  poles  lie  outside  of  the  space  between  the  planes  of  the  electrodes  that 
significant  values  of  5  are  observed.  Figure  274a,  obtained  with  cylindrical 
pole  pieces,  is  a  summary  of  the  first  group  of  results  and,  as  it  happens,  the 
smoothest  thus  far  completed.  Both  branches  separated  by  the  crest  are 
nearly  linear.  Figure  2746  was  obtained  with  ball  poles.  The  anterior 
branch  is  still  linear,  but  the  rear  branch  has  an  unexpected  bulge  upward  at 
%  =  $.  Figure  275a  is  a  careful  repetition  of  this  group  of  measurements. 
The  double  inflection  between  x  =  4  and  5  cm.  is  not  removed  and  the  last 
5  values  relatively  low.  As  the  fringe  displacement  5  is  not  steady,  but 
fluctuating,  for  reasons  referable  only  to  the  generator,  it  seemed  useless  to 
endeavor  to  go  further  without  overhauling  the  machine. 

Some  of  the  tin  plates  of  the  ^Vimshurst  having  become  damaged  in  use, 
these  were  replaced  and  a  few  other  alterations  made.  Figure  2756  sum¬ 
marized  the  new  result.  The  crest  is  over  30  per  cent  higher  than  in  the 
earlier  cases,  evidencing  the  marked  improvement  in  the  efficiency  of  the 
machine  and  the  graph  is  again  regular,  with  two  approximately  linear 
branches  on  each  side  of  the  crest;  the  latter  has  shifted  somewhat  to  the  right. 
Nevertheless,  the  fluctuation  of  5  values,  apparently  due  to  casual  partial 
internal  discharges  of  the  machine,  was  not  improved  and  remains  outstanding. 

As  a  crest  invariably  appears  in  all  the  curves,  it  seems  obvious  to  refer 
it  to  the  limiting  potential  of  the  machine.  After  the  maximum  sparking 
distance  x  is  passed,  the  strength  of  the  field  (kilovolts/cm.)  between 
electrodes  rapidly  diminishes  until  it  reaches  a  threshold  field-strength  ineffec¬ 
tive  in  5.  Furthermore,  5  is  an  expression  for  the  convection  current  if  the 
same  electrode  is  used.  Hence,  the  ^-graphs  give  indications  of  both 
potential  and  current  values,  but  not  simply. 

94.  Mucronate  electrode  with  micrometer — The  adjustment  is  shown 
in  the  insert,  figure  278,  where  the  electrode  Ef  is  attached  to  the  one-quarter 
inch  brass  tube  a,  partially  stopped  at  c  by  a  perforated  cylinder.  The 
tube  a  contains  the  micrometer  screw  6,  the  end  of  which  is  tipped  by  the 
needle  n.  Hence,  by  turning  6,  the  point  n  may  be  moved  from  within  E'c 
and  made  to  project  by  any  small  amount  beyond  it.  The  zero  of  this  appara¬ 
tus  is  arbitrarily  found  at  the  position  of  the  micrometer-screw  (reading 
y ),  at  which  pressure  5  suddenly  begins  to  appear  at  E.  Before  this  sparks 
or  sparklets  continually  jump  across  from  Ef  to  E  and  5  =  0.  The  first  5 
for  y  =  o  is  casual,  the  fringe  displacement  5  appearing  and  vanishing  alter¬ 
nately  with  much  interferometer  turmoil.  Immediately  thereafter  (fig.  276), 
y  increasing,  5  is  definite  and  near  the  maximum,  which  here  seems  to  occur 
for  a  projection  of  Ay  =  0.06  — 0.03  =0.03  cm.,  since  at  ^  =  0.03  cm.,  s  =  o. 
Figure  276  gives  two  examples  of  the  cuspidal  graphs.  Almost  half  the 
efficiency  is  lost  after  this  projection  y  —  2  mm.,  but  this  is  a  moderate  result 
as  compared  with  the  following. 

The  relatively  low  5  values  in  figure  276  indicated  some  maladjustment. 


PROBE  AND  THE  INTERFEROMETER  U-GAGE 


151 


The  electrodes  E  and  E'  were  therefore  freshly  turned,  polished,  and  adjusted 
more  fully  in  parallel.  The  effect  of  this  is  astonishing,  as  shown  in  the  graphs, 
figure  278.  Both  graphs  drop  from  an  actual  cusp;  for  the  initial  data  were 


y= 0.02 
s=  o 


0.025  0.03  0.04  cm.l  . 

560  520  480  / 


At  7  =  0.025  the  sparking  is  intermittent,  so  that  it  is  difficult  to  catch  the 
fringes  between  sparks.  At  7  =  0.02,  5  =  0,  and  therefore  the  point  of  the 
needle  is  just  within  the  effective  limit  of  the  disk  electrode.  Hence,  the 
cusp  appears  within  a  tenth  of  a  millimeter  from  the  critical  boundary  of 
the  disk  and  is  70  per  cent  higher  in  5  than  the  crest  of  figure  275.  Had  it 
been  possible  to  approach  the  surface  closer,  there  is  no  doubt  that  a  higher 
order  of  5  values  would  have  been  obtained.  The  field  for  £  =  2  cm.  may  be 
estimated  as  10  kv./cm.,  insuring  the  stream  of  ions  just  before  sputtering. 

The  corresponding  phenomena  for  other  spark-gap  (x)  values  are  now  to 
be  treated.  In  figure  279,  curve  a,  x  =  1  cm.,  while  y  increases  from  o  to  0.32 
cm.  At  this  small  distance  sparks  readily  jump  across,  even  when  7  =  0.05 
cm.,  and  they  pass  between  parts  of  the  electrodes  rather  than  from  the 
appreciably  salient  needle-point.  At  times,  sparking  may  suddenly  cease, 
whereupon  high  pressure  (s)  takes  its  place.  This  was  the  case  with  the 
first  points  (7  =  0.06  or  less)  in  figure  277.  Thus  there  is  no  doubt  that  this 
graph  is  cuspidal,  though  it  can  not  be  tested.  The  5-drop  with  increasing 
y  is  naturally  fast,  and  5  =  0  would  soon  occur,  since  x  —  y  is  small. 

The  case  for  #  =  4  cm.  (fig.  279,  curve  b)  differs  from  curve  a ,  as  in  the 
former  the  cusp  seems  to  be  actually  rounded.  The  height  5  of  the  crest, 
moreover,  is  less  than  was  expected  (cf.  fig.  275  a,  b),  which  leads  me  to 
suspect  that  the  adjustment  was  somehow  less  accurate.  The  fall  is  relatively 
slow. 


95.  Contributory  results — Some  relevant  measurement  of  the  potential 
variation  of  the  machine  is  desirable  to  account  for  the  preceding  results. 
These  data  were  obtained  with  a  simple  electrometer  in  which  the  indications 
were  given  by  the  deflections  of  a  light  horizontal  flexure  needle  of  aluminum. 
It  was  not  thought  necessary  to  standardize  the  apparatus,  as  the  deflections 
suffice  the  present  purposes.  One  pole  of  the  Wimshurst  machine  was  put 
to  earth  and  the  other  joined  to  the  electrometer.  An  example  of  the  results 
is  given  in  figure  280,  in  which  the  potential  is  rated  in  arbitrary  scale-parts 
for  different  widths,  x,  of  mucronate  spark-gap.  The  graph  V  shows  the  free 
potential  with  the  machine  making  6  rotations  per  second.  Vr  is  the  residual 
potential  retained  after  the  machine  comes  to  rest  (r/t  =  o)  without  being 
discharged.  This  is  the  threshold  potential  and  the  electric  wind  of  the  pre¬ 
ceding  paragraphs  does  not  blow  (5  =  0)  until  this  potential  is  exceeded. 
One  may  note  in  particular  that  V  is  constant  after  #  =  1.5  cm.  for  the  mucro¬ 
nate  electrode  used.  For  £<1.5  cm.  the  V  and  Vr  values  are  coincident  and 
fall  off  very  rapidly. 


152 


ACOUSTIC  EXPERIMENTS  WITH  THE  PIN-HOLE 


If  we  write  F=V/x,  treating  the  axial  field  F  as  uniform,  the  graphs 
F  and  Fr  are  obtained.  Both  curves  have  their  crests  at  x  =  i  cm.,  which 
should  therefore  be  the  strongest  field  used.  The  preceding  experiments 
(figs.  274,  275,  etc.)  reach  their  crests  at  x  =  2  to  2.5  cm.,  therefore,  in  a 
materially  weaker  field  F.  It  is  to  be  observed,  however  (see  fig.  271),  that 
for  x  =  1,  the  electrodes  are  already  so  close  together  that  the  electric  wind 
must  in  large  measure  be  not  axial  but  radially  outward.  Hence,  only  a 
component  pressure  acts  at  the  electrode  E.  Not  until  the  value  of  %  has 
become  larger  (x>  2  cm.)  will  the  wind  in  the  main  be  axial.  This  at  least 
seems  to  be  the  most  plausible  method  of  accounting  for  the  5#  crests  in 
question  (cf.  fig.  282),  the  electric  wind  being  a  vortex-ring  whose  plane  is 
parallel  to  the  electrodes  and  whose  axis  of  symmetry  is  the  needle. 


It  is  somewhat  surprising  that  the  limiting  potential  is  practically  inde¬ 
pendent  of  the  speed  of  the  machine.  Thus  far,  spark-gaps  #  =  1.5,  2.0,  and  4.0 
cm.,  each  at  rotations  1.5,  3,  and  6  rot./sec.,  the  same  limiting  potential,  V  =  3, 
was  built  up,  more  gradually  of  course  for  the  slower  motions.  For  x—i  cm., 
the  limit  was  V=i.2  independent  of  the  speed  of  rotation.  For  #  =  0.5  cm., 
V  =  o.  Thus  the  excess  potential  is  removed  by  the  leakage  of  the  spark- 
gaps  like  the  mucronate  electrode,  or  at  other  incidental  saliences  of  the 
machine.  The  electric  wind  appears  in  the  nature  of  a  current  running  through 
the  machine.  One  can  hardly  expect  50c  i/x,  however,  and  the  graphs  for 
x>2  conform  more  nearly  to  s0— s «  %. 

The  size  of  the  hole  in  the  electrode  E  (fig.  270)  is  of  little  consequence. 
Closed  with  a  flat,  smooth-headed  brass  nail,  loosely,  the  same  5  values  were 
obtained. 

Using  a  still  smaller  Wimshurst  machine,  the  character  of  graphs  remained 


PROBE  AND  THE  INTERFEROMETER  U-GAGE 


153 


the  same,  but  the  5  values  were  much  reduced.  Examples  are  given  in  figure 
281,  in  which  the  curve  a  has  a  longer  pointed  mucronate  electrode  than  b. 
The  crests  are  again  at  x  =  2  cm.  Judging  from  sparks,  the  potentials  fur¬ 
nished  by  the  machines  were  larger  for  the  small  machine.  But  the  plates 
of  the  smaller  machine  were  less  than  0.8  of  the  diameter  of  larger  and  the 
former  could  be  rotated  at  only  3  r/sec.  The  available  electric  currents, 
and  hence  the  corresponding  5 ,  differ  largely.  Hence,  5  may  again  be  regarded 
as  responding  to  the  current  flowing  in  and  out  of  the  machine  after  the 
residual  potential  is  exceeded. 

Using  the  aluminum  electrometer,  the  potentials  came  out  as  about 
4.0  for  the  smaller  to  3.0  for  the  larger;  but  the  currents  5  run  as  5  =  250  to 
600  for  the  larger,  compared  with  5  =  60  for  the  smaller  in  the  above  graphs. 

The  endeavor  to  use  the  mucronate  electrode  in  case  of  an  induction- 
coil  just  below  sparking,  in  a  given  gap,  did  not  succeed.  Values  of  5  between 
5  =  7  and  15  (in  later  experiments  5  =  30)  only,  could  be  obtained  for  £  =  3.5 
cm. ;  and  there  was  even  then  incipient  sputtering,  which  is  fatal  to  large  5. 

It  remains  to  determine  the  effect  of  the  speed  of  rotation  (r/sec.)  of  the 
given  electric  machine  on  the  5  values.  This  is  a  complicated  question,  for 
the  answer  depends  on  the  incidental  charge  of  the  machine,  as  well  as  on 
r/sec.  I  endeavored  to  overcome  the  uncertainty  by  rotating  for  some  time 
in  each  case,  hoping  that  in  this  way  (beginning  with  the  charge  zero)  the 
normal  condition  would  be  established.  The  results  are  given  in  figure  282, 
which  contains  both  s ,  rot./ sec.,  and  sx-graphs. 

When  %  is  constant,  5  increases,  nearly  proportionally  to  the  angular 
velocity  of  the  plates,  1.5,  3,  and  6  rotations  of  each  plate  per  second  being 
instanced.  The  lines  pass  through  zero  as  x  increases  from  o  to  1  to  2  cm., 
the  optimum  spark-gap.  The  rates  at  which  5  increases  with  r/sec.  thus 
steadily  increase.  After  this  (x  =  2  to  4  cm.)  the  line  merely  drops,  the  rate 
of  5  increases,  with  r/sec.  remaining  about  the  same.  Thus,  for  instance, 
if  £  =  4  cm.,  1.5  rotations  per  second  leave  5  unchanged  at  zero. 

The  effect  of  this  on  the  sx  graphs  is  apparent.  Figure  282  shows  that 
the  crests  persist  at  x  =  2  cm.,  but  that  the  graphs  drop  as  a  whole  when 
r/s  diminishes  from  6  to  3  to  1.5. 

96.  Velocity  of  the  winds — An  estimate  may  perhaps  be  obtained  if  we 
use  Bernoulli’s  equation  and  put  v  —  yj  2 p/p.  In  the  graphs,  figures  269 
to  276,  the  5  values  at  crests  are  very  commonly  5  =  300,  and  they  mount  to 
even  5  =  550.  Since  the  unit  of  5  is  about  io~6  atm.,  these  data  may  at  once 
be  taken  as  pressures  in  dynes/cm2.  Thus  the  velocities  in  the  two  cases 
are  roughly  v  =  7 70  cm./ sec.  frequently  and  v  =  1 ,000  cm./ sec.  in  very  favorable 
cases.  These  are  astonishingly  large  values.  In  the  small  time  of  x/v,  where 
x  =  6  cm.,  there  is  very  little  time  for  the  decay  of  ions.  The  change  of  5  with 
x  is  thus  to  be  associated  with  a  ring-shaped  vortex  of  air,  whose  axis  is  the 
needle  prolonged.  Hence  the  currents  near  the  electrode  E ,  when  x  is  small, 
must  be  largely  radial  and  outward,  as  already  instanced. 


154 


ACOUSTIC  EXPERIMENTS  WITH  THE  PIN-HOLE 


When  the  needle  retreats  into  the  effective  confines  of  the  E'  electrode, 
the  latter  begins  to  sputter.  At  small  distances  sparks  may  pass  across. 
The  pressure  5  drops  to  zero  very  nearly.  This  sputtering  immediately 
following  high  s  values  when  y  is  small  is  very  interesting,  since  it  recalls  the 
behavior  of  the  sensitive  flame  in  acoustics.  Here  also  a  uniform  linear 
column  breaks  down  into  an  oscillating  column.  Hence,  one  is  tempted  to 
conclude  that  in  sputtering  the  ionized  winds  may  be  treated  as  alternately 
positive  and  negative  and  hence  produce  no  pressure  at  E.  The  phenomenon 
is  not  an  electric  oscillation,  of  course,  as  its  frequency  must  conform  to  the 
motion  of  air-currents. 

If  we  take  0  =  1,000  cm./ sec.,  the  maximum  estimated  above,  the  limiting 
frequency  would  be  n  =  v/2X  and  hence,  if  the  spark-gap  is  x  —  2  cm.,  n  —  250 
or  about  c'  of  the  2 -foot  octave.  This  is  naturally  much  too  high,  say  ten 
times;  but,  on  the  other  hand,  an  immediate  reversal  of  alternating  air- 
currents  is  improbable,  so  that  the  relations  are  not  out  of  the  question. 
It  is  curious  that  sputtering  frequently  occurs  for  a  slow-moving  machine 
and  will  cease  when  the  machine  moves  faster. 

Alternatively  one  may  simply  assert  that  the  field  insulation  breaks 
down  when  the  electrical  pressure  or  field  potential  energy,  F2/ Sir,  has  reached 
a  certain  value.  The  energy  which  drives  the  air-current  is  then  converted 
into  the  heat  of  the  minute  sparks  and  the  electric  wind  ceases.  With  regard 
to  the  electrical  circuit,  we  may  thus  conclude  that  in  the  absence  of  sputter¬ 
ing,  the  ions  are  taken  from  E'  to  E  by  air  convection;  hence  the  pressure,  5. 
On  the  other  hand,  when  sputtering  occurs  and  5  =  0,  the  electric  current 
phenomenon,  is  akin  to  the  conduction  of  electricity  in  electrolytes,  though 
with  far  more  tempestuous  collision  of  ions,  as  these  are  shot  at  each  other 
with  a  velocity  (according  to  the  above  estimates)  somewhat  short  of  1,000 
cm./sec.  There  is  no  electric  wind  (5  =  0),  in  spite  of  the  appearance  in  the 
dark  of  a  current  of  sparklets  from  Ef  to  E. 

A  series  of  experiments  in  which  the  actual  saliency,  y'f  of  the  needle 
from  the  plane  of  the  electrode  E'  was  measured  (in  the  above  graphs,  figure 
279,  the  y  =  o  refers  to  the  first  occurrence  of  sputtering)  gave  the  following 
data: 

x  =  2\y'  =0.03  0.05  0.06  0.07  0.11  0.19  0.27  cm. 

s=  o  o  570  478  324  188  138 

also  summarized  in  figure  277,  on  a  reduced  scale.  Thus  sputtering  begins 
when  the  needle  protrudes  half  a  millimeter  from  the  electrode.  Endeavors 
made  to  sharpen  the  rather  fine  needle  brought  no  consistent  results. 

A  needle  placed  in  the  U-tube  electrode  produced  only  a  just  perceptible 
negative  pressure. 

97.  A  method  for  measuring  the  energy  of  X-rays.  Introductory  appa¬ 
ratus — This  important  problem  has  recently  been  attacked  with  surprising 
success  by  Mr.  H.  M.  Terrill,  who  gives  references  to  the  earlier  work.  He 
uses  a  bolometric  method,  and  constructs  an  apparatus  which  should  be 


PROBE  AND  THE  INTERFEROMETER  U-GAGE 


155 


generally  available  in  the  laboratory,  provided  the  extremely  delicate  con¬ 
ditions  of  constant  environmental  temperature  can  be  met.  I  had  been 
working  on  an  air-thermometer  method  when  Mr.  Terrill’s  results  appeared; 
but  I  have  not  thus  far  obtained  anything  separable  from  temperature 
effects,  at  least  from  the  rather  primitive  X-ray  generator  which  I  used. 
Moreover,  it  is  not  probable  that  any  results  worth  recording  will  be  obtain¬ 
able  in  a  steam-heated  room.  In  the  summer  time,  however,  I  think  the 
method  should  be  feasible  in  a  basement  room,  so  that  a  brief  account  of 
the  method  may  be  given  here.* 

In  figure  283,  U,  U'  is  the  interferometer  U-tube,  the  closed  shanks  of 
which  are  provided  with  the  tubulures  t  t\  each  carrying  a  lateral  branch 
with  a  stopcock,  c ,  c'.  The  tubes  t  and  t'  communicate  with  the  boxes  A 
and  B  of  thin  waxed  wood  or  aluminum,  about  10.6X6.2X7.8  cm.,  or  517 
cm3,  in  volume.  To  this  must  be  added  the  volume,  v,  above  the  mercury 
surface,  69  cm3.,  making  a  total  of  586  cm3,  as  the  effective  volume  in  each  of 
the  closed  regions. 


Whereas  the  box  B  is  empty,  the  box  A  is  provided  with  a  succession  of 
metallic  curtains,  alternating  and  extending  not  quite  across  the  box,  prefer¬ 
ably  of  lead.  But  as  the  lead  foil  available  was  not  thin  enough,  12  sheets 
of  copper  foil,  each  0.004  cm.,  thick  were  used  instead.  The  boxes  AB  were 
surrounded  by  a  heavy  metallic  case,  DE,  the  inside  of  which  was  filled  with 
cotton  batting,  on  which  the  boxes  reposed.  On  the  side  to  be  illuminated 
by  the  X-rays,  X  X',  however,  there  was  a  clear  space,  ab ,  a'b ',  for  the  intro¬ 
duction  of  the  radiation,  paper  screens  being  provided  to  obviate  air-currents. 

Thus  it  was  supposable  that  whereas  both  chambers  A  and  B  would 
absorb  heat  radiation  under  like  conditions,  the  A  chamber  only  (supposing 
the  metal  sheets  sufficiently  thick  in  the  aggregate)  would  absorb  the  X- 
radiation.  The  heat  produced  in  this  way  would  correspondingly  increase 
the  pressure  on  that  side.  One  may,  therefore,  when  A  receives  radiation 

*H.  M.  Terrill,  Phys.  Rev.,  vol.  28,  p.  438,  1926 


156 


ACOUSTIC  EXPERIMENTS  WITH  THE  PIN-HOLE 


(X),  close  the  cock  c  and  open  c',  and  when  B  receives  radiation  ( X ')  close 
c'  and  open  c;  or,  preferably,  close  both  stopcocks  c  and  c'  and  let  the  radia¬ 
tion  X  be  received  symmetrically  by  A  and  B.  In  the  latter  case  the  thermal 
effects  balance  each  other,  whereas  the  X-ray  effects  heat  A  only.  The  total 
mass  of  the  copper  sheets  was  28.7  g.  There  were  12  sheets  about  6  by  10 
cm2,  in  area.  As  each  sheet  is  0.004  cm.  thick,  this  makes  a  total  thickness  of 
half  a  millimeter  of  copper  only,  which  is  inadequate  for  complete  absorption, 
but  may  be  used  for  orientation.  Lead,  in  addition  to  its  density,  would 
have  the  further  advantage  of  low  specific  heat. 

98.  Computation — It  will  first  be  necessary  to  ascertain  what  tempera¬ 
ture  increment  in  A  corresponds  to  the  passage  of  one  fringe.  In  order  to 
obtain  an  estimate,  we  may  regard  the  whole  region  A  to  be  at  the  same 
temperature,  as  the  volume  in  the  gage  is  but  12  per  cent  of  the  whole.  If 
v  is  this  volume,  V  being  the  volume  of  the  box  A,  p,  m,  r,  the  pressure  mass 
and  absolute  temperature  of  the  air,  initially 

(1)  p(v  -f-  V)  =  R  m  t 

As  the  change  of  temperature  is  very  small,  we  may  neglect  squares  of  small 
quantities  and  differentiate  logarithmically,  whence 

/  N  Ap  Av  At 

W  —  +  —T7,  =  — 

p  V  +  V  T 

Here,  Ap/p  =  Ah/h,  the  ratio  of  mercury  heads,  h  being  the  barometric  height. 
Av  is  equal  to  irr2Ah/2  if  r  is  the  radius  of  U,  since  but  half  the  mercury  depres¬ 
sion  is  on  the  pressure  side.  Finally,  v  =  irrH ,  if  t  is  the  thickness  of  the  air¬ 
space  in  U.  Hence: 

(3)  AT  =  TAh(—  d - - - ^ 

\h  2  (2  +  V  /  7JT2)  / 

But  Ah  per  fringe  is  X/2  cos  <p,  where  <£>  =  45°  is  the  angle  of  incidence  of 
rays.  This  is  equivalent  to  about  Ah  =  42  Xio'6  cm.  of  mercury,  or  5.5  Xio-7 
atm.  per  fringe.  Thus,  if  h  —  76  cm.,  7  =  300°,  t  —  1  cm.,  F=  517  cm3.,  r  =  4.7 
cm.,  \  =  6Xio-5  cm. 

(4)  Ar  =  8.6 Xio-4  °C.  per  fringe 

Since  the  thermal  discrepancies  are  supposed  to  balance  in  A  and  B, 
the  X-radiation  absorbed  in  A  may  be  computed  as  AH  =(ma-\-m's')AT 
where  m  is  the  mass  and  a  the  specific  heat  of  the  metallic  curtains.  To  this 
the  mass,  m'}  and  specific  heat  0',  of  the  air  within  A  is  to  be  treated  as  a 
correction.  Putting  m  =  28.7  g.,  <7  =  0.091,  m' =  0.62  g.,  <r'  =  o.24,  AH  =  (2.6i  + 
0.15)  Ar  per  fringe,  or  with  the  given  value  of  At  in  (4) 

AH  =  2.4 Xio-3  ca./fr.  =  io5  ergs  per  fringe. 

If  we  take  the  mean  datum  for  the  X-ray  energy,  trapped  by  Mr.  Terrill, 
H  =  3.9  X  io6  ergs  in  5  min.,  or  7.8  X  io5  ergs/min.,  one  ought  to  expect  H/AH  — 
7.8  fringes  per  minute,  or  about  78  fringes  in  a  run  of  10-minute  periods. 


PROBE  AND  THE  INTERFEROMETER  U-GAGE 


157 


As  the  X-rays  here  in  question  are  intense,  it  is  thus  only  under  conditions 
of  exceptionally  constant  temperatures  in  the  environment  that  trustworthy 
data  can  be  looked  for,  even  if  a  somewhat  larger  solid  angle  is  in  question  in 
the  above  apparatus. 

99.  Data — A  large  number  of  experiments  were  made,  both  with  and  with¬ 
out  X-radiation,  in  the  endeavor  to  minimize  the  temperature  discrepancy. 
These,  however,  led  to  no  trustworthy  results,  and  it  seems  impossible,  in  the 
winter  time  and  in  a  heated  room,  to  control  the  temperature  effect.  I  shall 
merely,  in  figure  284,  give  an  example  of  a  typical  run  without  X-rays.  Here 
5,  or  1.4  times  the  number  of  fringes,  is  the  ordinate.  The  weather  being 


warm,  the  room  was  heated  in  the  morning  only  and  again  in  the  late  after¬ 
noon.  After  the  steam  was  turned  off,  the  apparatus  (including  the  U -gages, 
covered  on  all  sides  with  metal  box  and  wadding)  settled  into  a  steady  state 
between  (a)  and  ( 6 ).  Thereafter,  with  the  inflow  of  steam  heat  at  (6),  the 
thermal  variation  recommences. 

In  the  same  diagram  I  have  inserted  (fig.  285)  the  above  rise  of  temperature 
reduced  to  5  (5  =  4.6  per  minute),  to  be  anticipated  from  strong  X-rays. 
It  appears  that  in  the  summer  time,  in  a  good  basement  room,  the  experiment 
should  be  feasible,  and  it  was  therefore  postponed  for  the  present. 

100.  Apparatus.  Results.  Modified  u-gage — This  modification  con¬ 
sists,  as  shown  in  figure  286  (where  BB'  is  the  cast-iron  body  of  the  shallow 
U-gage,  66'  the  mercury  content,  the  pools  being  connected  by  the  narrow 
channel  r,  and  aa'  the  cover-glasses  of  the  reservoirs,  10  cm.  in  diameter  and 


158 


ACOUSTIC  EXPERIMENTS  WITH  THE  PIN-HOLE 


about  i  cm.  deep),  in  floating  the  two  plate-glass  disks  c,  c'  only  about  5  cm. 
in  diameter  on  the  respective  and  much  wider  mercury  surfaces.  The  disks 
are  kept  in  place  by  platinum  stems  cemented  to  the  middle  of  the  lower 
sides  of  c  and  c'  and  projecting  downward  into  the  depressions  e ,  e'  drilled 
into  the  body  B,  B\  at  the  centers  of  the  pools.  Short  tubulures  t,  t'  com¬ 
municate  with  the  atmosphere. 

In  a  gage  so  constructed  it  was  thought  that  the  surfaces  c  and  c'  would 
remain  more  rigorously  in  parallel  for  relatively  large  displacements.  The 
tests  showed  that  the  general  manipulations  were  not  much  more  difficult 
than  with  the  older  gage  with  large  plates  c  c'.  In  other  words,  there  was  no 
unreasonable  quiver  of  fringes,  unless  an  excess  of  mercury  charge,  bb',  had 
been  introduced. 

Two  fatal  discrepancies,  however,  soon  showed  themselves.  In  the  first 
place,  the  floating  glass  plates  c  c'  would  have  to  be  rigorously  plane  parallel ; 
otherwise  any  rotation  of  c  relative  to  c'  around  a  vertical  axis  would  be  apt 
to  change  the  fringes,  both  as  to  size  and  inclination,  enormously.  Rotations 
of  this  kind,  moreover,  would  be  almost  inevitably  incident  to  the  usual  run 
of  experiments. 

The  other  is  the  hysteresis-like  error  reproduced  in  figure  287.  When 
the  fringe  displacement  5  increases,  the  5  values  are  too  small,  and  when  it 
decreases  5  values  are  too  large,  and  this  in  spite  of  the  vigorous  tapping 
under  which  each  of  the  observations  were  made.  Without  tapping  the 
results  would  have  been  chaotic,  whereas  in  the  old  gage  tapping  is  rarely 
necessary.  Supposing  that  the  change  of  mercury  was  insufficient  (i.  e.,  the 
pools  too  shallow),  an  excess  charge  was  introduced.  Observation  was  now 
inconvenienced  by  the  tendency  of  fringes  to  quiver;  but  the  graph,  figure  288, 
was  obtained  in  this  way.  Hysteresis  has  in  fact  diminished,  but  it  is  still 
prohibitive  and  the  annoyance  of  tapping  the  gage  interferes  with  its  use 
when  continuous  phenomena  are  to  be  observed. 

If  we  inquire  into  the  reason  for  the  behavior  in  question,  it  seems  obviously 
referable  to  friction.  Probably  a  film  of  air  collects  around  the  stem  and 
walls  of  the  cavities  e ,  ef.  When  the  stem  approaches  the  walls,  therefore, 
it  would  be  held  against  them  by  mercury  pressure  in  virtue  of  the  usual 
capillary  phenomena.  Steps  were  therefore  taken  to  remove  all  air-films  by 
charging  the  mercury  in  vacuo.  Unfortunately,  the  plate  a',  owing  probably 
to  some  molecular  strain,  failed  to  sustain  the  air-pressure  long  enough  for  a 
full  test  and  the  gage  was  completely  wrecked  by  the  explosion.  A  new  gage 
with  new  plates  was  then  constructed  and  carefully  exhausted  many  times. 
The  new  results,  however,  were  in  no  wise  superior  to  the  summary  in  figures 
287  and  288.  If  anything,  they  were  worse.  Tapping  was  absolutely  essen¬ 
tial.  The  stem  method  of  anchoring  the  floating  plates  is  thus  impractical, 
even  if  the  extra  quiver  of  the  mercury  with  small  plates  is  admitted. 


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